# Deep Space Network as a Queue: Contention, Wait-Time, and the Science-Throughput Penalty of Antenna Scheduling


**A Doctoral Dissertation**

**Candidate:** JPL_INSTRUMENTS_NAV_05

**Program:** COLLEGIUM 1st Battalion

**NORTH STAR / JPL Category:** Navigation and Guidance

**Hall-of-Shoulders Anchors:** Jay W. Forrester (system dynamics: stocks, flows, delayed feedback, counterintuitive concentration); Nassim N. Taleb (fat tails and fragility: test-do-not-assume, the convex load-response); the queueing-theory tradition (Kendall, Kleinrock, Terekhov et al.); and the heavy-tail estimation lineage (Clauset-Shalizi-Newman, powerlaw, poweRlaw, extreme-value peaks-over-threshold).

**Stage:** Design-stage analysis plan. No Deep Space Network scheduling log has been analyzed; every empirical magnitude in this document is an illustrative placeholder labeled as such at the point of use.

**Date:** 2026-06-15


## Abstract

The Deep Space Network (DSN) is a shared inheritance held in common by the agency's missions: the ground asset that provides tracking, telemetry, and command for nearly every NASA deep-space mission and for many partner missions, and that asks to be stewarded as carefully as it is used. Its three complexes at Goldstone, Madrid, and Canberra hold a fixed number of antennas, while the population of supported missions and their aggregate data-return requirements keep growing, so demand for tracking passes exceeds supply during recurring windows and the schedule that allocates antenna time becomes a contested resource. This dissertation treats the DSN as a queueing system in which mission requests wait for allocation and some requested passes are never served, and it asks one question: is the science-throughput penalty caused by this contention distributed uniformly across requests, as a simple congestion picture would imply, or is it heavy-tailed and concentrated on identifiable orbital-geometry and mission-phase windows?

The falsifiable contribution is a pair of competing hypotheses. The null (H0) holds that scheduling friction is roughly uniform, that request-to-allocation wait times and pass-loss events are light-tailed, and that no small share of geometry, band, or phase windows accounts for a disproportionate share of lost downlink. The alternative (H1) holds that the wait-time and pass-loss distributions are heavy-tailed and that a minority of windows drives a majority of the lost science return. The contribution is accepted only if both the wait-time-tail clause and the concentration clause pass their pre-registered tests; either failing refutes it. The method combines survival analysis of the time from request submission to allocation or expiry (Kaplan-Meier and Cox proportional hazards with time-varying load), heavy-tail distribution fitting against an exponential null (Clauset-Shalizi-Newman maximum-likelihood-plus-goodness-of-fit and generalized-Pareto peaks-over-threshold estimation), concentration measurement (Gini coefficient and top-decile window share), and regression of pass-loss on orbital geometry, frequency band, and concurrent-mission load under mission and epoch fixed effects. The named data are the DSN scheduling and tracking logs available through the service catalog and Service Preparation Subsystem archives, the NTRS DSN loading and forecasting reports, and the mission downlink-requirement records.

The theoretical frame is threefold and convergent. Queueing theory supplies the formal model of waits and deadline-driven losses and identifies three concurrent routes by which a moderately loaded server develops a heavy upper tail: hard viewing-window deadlines, bursty clustered arrivals, and skewed service requirements. Forrester's system dynamics supplies the structural reason concentration is plausible, namely looped and delayed feedback among locally optimizing missions that piles requests onto shared windows. Taleb's program supplies the statistical discipline, namely testing for fat tails rather than assuming them away and reading a convex load-response as the signature of fragility.

The work is presented honestly as a design-stage analysis plan; no empirical results are claimed as executed, and expected magnitudes are labeled illustrative throughout. Its payoff for NASA and JPL is to convert a known average shortfall into a decision-relevant shape: if the penalty is concentrated, targeted aperture, scheduling policy, and demand shaping at the carrying windows recover the most science return per dollar; if it is uniform, only broad capacity expansion helps. Either outcome is usable, and the crewed-exploration era is best planned against the load-response curve rather than a misleading average.


## Table of Contents

- **Front Matter**: Abstract; Table of Contents; List of Tables
- **Chapter 1. Introduction**
  - 1.0 The chapter's answer
  - 1.1 The Deep Space Network as NASA's most-shared navigation and communications asset
  - 1.2 Fixed supply, growing demand, and structural oversubscription
  - 1.3 From "oversubscribed" to a measurable distributional question
  - 1.4 The single falsifiable contribution
  - 1.5 Why it matters for NASA, JPL, and the named stakeholders
  - 1.6 Scope, delimitations, and the design-stage guardrail
  - 1.7 Definitions of key terms
  - 1.8 Roadmap of the dissertation
- **Chapter 2. Theoretical Framework**
  - 2.0 The chapter's answer, stated first
  - 2.1 The queueing lens: arrivals, servers, deadlines, and the tail of the wait
  - 2.2 Three DSN-specific routes to a heavy tail
  - 2.3 Forrester's lens: stocks, flows, delayed feedback, and structural concentration
  - 2.4 Taleb's lens: Mediocristan versus Extremistan, and the discipline of not assuming thin tails
  - 2.5 Synthesis: the integrated conceptual model the empirical work will test
- **Chapter 3. Literature Review**
  - 3.0 The chapter's answer, and the problem it addresses
  - 3.1 DSN scheduling as optimization: strong on mechanism, silent on the residual distribution
  - 3.2 DSN capacity and traffic forecasting: strong on aggregate loading, silent on the distribution over requests
  - 3.3 Ground-station and constellation contact-scheduling beyond the DSN: the same posture at larger scale
  - 3.4 The methodological literatures the dissertation imports, and where they have not yet been applied
  - 3.5 The gap, stated explicitly, and the propositions that follow
- **Chapter 4. Data and Measurement**
  - 4.0 The chapter's answer
  - 4.1 The problem this chapter addresses
  - 4.2 Named datasets in depth
  - 4.3 Units of analysis
  - 4.4 Variable construction and the measurement table
  - 4.5 Coverage requirement and panel assembly
  - 4.6 Data-quality and measurement limitations
  - 4.7 Access, data-use arrangements, and ethics
  - 4.8 Validation against known values
  - 4.9 Summary
- **Chapter 5. Research Design and Identification**
  - 5.0 The chapter's answer
  - 5.1 Estimands
  - 5.2 Estimators
  - 5.3 Identification strategy
  - 5.4 Model specifications
  - 5.5 Threats to validity
  - 5.6 Robustness battery
  - 5.7 Power and minimum-detectable-effect analysis
  - 5.8 Pre-registration commitment
  - 5.9 Computational and software plan
  - 5.10 Summary of the design
- **Chapter 6. Analysis Plan and Expected Results**
  - 6.0 The chapter's answer
  - 6.1 The problem this chapter addresses
  - 6.2 The five pre-registered estimation steps
  - 6.3 The heavy-tail fitting protocol
  - 6.4 The pre-registered decision rules
  - 6.5 The illustrative queueing simulation
  - 6.6 Expected findings, illustrative and not computed
  - 6.7 The event-study and loss-profile interpretation
  - 6.8 What a robust result would and would not establish
- **Chapter 7. Discussion**
  - 7.0 The chapter's answer, stated first
  - 7.1 Implications under a heavy-tail-and-concentration result (H1)
  - 7.2 Implications under a uniform result (H0)
  - 7.3 The theoretical contribution back to each anchor
  - 7.4 Rival explanations and how the design addresses them
  - 7.5 External validity and the crewed-exploration era
  - 7.6 Relationship to future capacity: optical communications and arraying as alternative supply levers
- **Chapter 8. Conclusion**
  - 8.0 The chapter's answer
  - 8.1 The problem this chapter addresses
  - 8.2 Restatement of the falsifiable contribution and the reframing
  - 8.3 What stands and what remains open at the design stage
  - 8.4 Both outcomes are useful: the symmetry that justifies the work
  - 8.5 Decision relevance for NORTH STAR navigation and guidance planning
  - 8.6 Future research: the path to executing the design on the full data
  - 8.7 Closing
- **References** (96 entries)
- **Appendices**
  - Appendix A. Variable and Data Dictionary
  - Appendix B. Derivations and Estimator Specifications
  - Appendix C. Instrument, Query, and Data-Access Details
  - Appendix D. Supplementary Tables


## List of Tables

- **Table 4.1.** Measurement codebook: construct, operational definition, source record, and scale (Chapter 4, Section 4.4.8).
- **Table D.1.** Notation register (Appendix D).
- **Table D.2.** Estimand-to-estimator-to-decision-rule crosswalk (Appendix D).

*No figures are included; the dissertation is a design-stage analysis plan and the result figures (survival curves, Lorenz-type concentration curves, load-response curves) are specified but unpopulated and described in Chapter 6.*



# Chapter 1: Introduction

## 1.0 The chapter's answer

This dissertation answers a single question, and the answer it defends can be stated before the question is even fully posed: the science-throughput penalty that the Deep Space Network (DSN) imposes through antenna-scheduling contention is, by the structure of the system that produces it, far more likely to be heavy-tailed and concentrated on a minority of orbital-geometry and mission-phase windows than to be smeared uniformly across all requests, and the difference between those two pictures bears directly on how the National Aeronautics and Space Administration (NASA) and the Jet Propulsion Laboratory (JPL) should spend constrained aperture, scheduling policy, and demand-negotiation effort. The contribution is a falsifiable distributional claim about the *shape* of that penalty, not a new scheduling algorithm and not a new capacity forecast. Where the operational literature reports the residual cost of contention as an aggregate satisfaction rate, which is a mean, this work asks whether the loss behind that mean is uniform (the null) or concentrated (the alternative), because the two cases imply opposite remedies. If the loss is uniform, only broad capacity expansion helps; if the loss is concentrated, a small targeted intervention recovers a large share of the lost science. The chapter develops that answer rather than withholding it. It states the problem in full, locates it in the institutional and historical record of the DSN, breaks the research question into explicit parts, names the stakeholders for whom the answer matters, fixes the scope and the design-stage honesty conditions, defines the key terms, states the single contribution as a pair of competing hypotheses, and then lays out the road the remaining chapters travel to test it.

A note on epistemic posture, made once here and carried throughout. This is a design-stage dissertation. No DSN scheduling log has been analyzed; no wait-time distribution has been fitted; no concentration coefficient has been computed. Every empirical statement about what the data would show is therefore an expectation derived from the structure of the system and from the behavior of analogous systems, not a finding. The confidence attached to the *mechanism* that predicts concentration is moderate-to-high, because three independent theoretical traditions converge on it; the confidence attached to whether the real DSN logs exhibit that concentration is, by construction, undetermined, and the entire research design exists to resolve it. The reader should read the word "would" in this chapter as load-bearing and deliberate.
## 1.1 The Deep Space Network as NASA's most-shared navigation and communications asset

The Deep Space Network is the single ground asset on which nearly every NASA mission beyond near-Earth orbit depends, and it is shared in a way that almost no other element of the agency's infrastructure is shared. An instrument held in common by so many missions carries a corresponding duty of stewardship, and that duty is the quiet premise behind everything that follows. A planetary orbiter, a cruising flyby spacecraft, a lander on the surface of another world, and a heliophysics observatory at a Lagrange point do not each command a dedicated ground station; they contend for time on a common pool of large-aperture antennas distributed across three complexes. Those complexes sit at Goldstone in California, near Madrid in Spain, and near Canberra in Australia, separated by roughly equal increments of terrestrial longitude so that a target anywhere in deep space is in view of at least one complex as the Earth rotates [\[10\]](#ref-10), [\[34\]](#ref-34). Each complex hosts one 70-meter antenna and several 34-meter antennas, and the network as a whole routinely serves several dozen missions at once [\[32\]](#ref-32). The DSN therefore occupies a structural position that makes its scheduling a portfolio-level problem rather than a mission-level one: a decision to allocate an antenna-hour to one spacecraft is, of necessity, a decision to withhold it from every other spacecraft that wanted the same hour on the same antenna in the same band.

What the DSN provides is not one service but three, and all three flow through the same contested aperture. The first is telemetry downlink, the return of science and engineering data from the spacecraft to the ground. The second is command uplink, the transmission of instructions and sequences from the ground to the spacecraft. The third, and the one most directly relevant to this dissertation's home category of navigation and guidance, is radiometric tracking: the precise measurement of Doppler shift and signal round-trip range that feeds orbit determination. These three are not interchangeable, and they do not all tolerate delay equally. A telemetry pass that is shortened loses some bits but may still return useful science; a command pass that is missed during a critical sequencing window can imperil a maneuver; a radiometric tracking pass that is lost during a trajectory-correction or encounter phase degrades the navigation solution at exactly the moment the solution matters most. The claim that the DSN is "the most-shared navigation and communications asset" is therefore not rhetorical inflation. It describes a real coupling: the same fixed set of antennas simultaneously carries the agency's deep-space data return and the agency's deep-space navigation, and contention for that aperture is contention for both at once.

The historical record shows how long this sharing has been the operating condition. The large-aperture antennas that anchor the network were built across decades, beginning with the first large Cassegrain antenna, Deep Space Station 11 (Pioneer), and extended through the family of high-efficiency 34-meter stations such as Deep Space Station 15 (Uranus), the first 34-meter high-efficiency antenna [\[72\]](#ref-72), [\[73\]](#ref-73). The 70-meter stations themselves are extensions of earlier 64-meter antennas, enlarged to recover link margin as missions traveled farther and demanded more [\[74\]](#ref-74). The point of recalling this lineage is not antiquarian. The supply side of the DSN has always grown in discrete, expensive, slow increments, each one a major capital project, while the demand side has grown continuously and, in recent years, sharply. A network whose capacity arrives in occasional large lumps and whose demand arrives in a steady and accelerating stream is a network that spends most of its life oversubscribed. The institutional history is, in effect, a long record of demand outrunning a supply that can only be increased in punctuated steps.

## 1.2 Fixed supply, growing demand, and structural oversubscription

The defining tension of DSN operations is the mismatch between a supply that is fixed over any planning horizon of interest and a demand that is not. Over the timescale on which scheduling decisions are actually made, weeks to a year, the number of antennas, their apertures, and their band coverage are constants. New antennas take years to design, fund, and commission; arraying existing antennas to synthesize a larger effective aperture is a real lever but a bounded one [\[71\]](#ref-71). The supply curve, in other words, is vertical on the operational horizon. The demand curve, by contrast, has been shifting outward along several axes at once, and the operational literature has documented the shift in detail.

The first driver is the sheer growth in the number of spacecraft. The advent of deep-space small spacecraft, exemplified by Mars Cube One, Lunar Trailblazer, Janus, the Escape and Plasma Acceleration and Dynamics Explorers, and the thirteen secondary missions carried on Artemis 1, has opened the prospect that a much larger number of deep-space spacecraft will be launched over the coming decade and beyond [\[35\]](#ref-35). A larger population of spacecraft means a larger population of tracking requests, and because small spacecraft do not bring their own ground infrastructure, those requests land on the same shared antennas. The second driver is the growth in per-mission data return. As instruments produce more data and as spacecraft fly higher-rate links, each mission's downlink requirement rises, so even a constant spacecraft count would impose a rising aggregate demand for antenna-time. The most recent JPL traffic studies, which model projected future-mission demand on the DSN out to a thirty-year horizon, identify exactly this combination: unparalleled growth in the number of robotic spacecraft, the emergence of relatively short but tracking-intensive human lunar exploration missions in the coming decade followed by an increasing cadence of robotic and then human missions to Mars, and dramatic increases in data rate and associated data volume [\[31\]](#ref-31). The third driver is the entry of crewed exploration traffic, which is not merely additional load but a different *kind* of load: high-rate, time-critical, and intolerant of deferral [\[17\]](#ref-17). A crewed lunar pass cannot be pushed to next week the way a routine cruise pass sometimes can.

When demand of this kind presses against a vertical supply curve, the result is structural oversubscription: in recurring windows the sum of requested antenna-time exceeds the available antenna-time, and the schedule must decide which requests are served in full, which are reduced, and which are dropped entirely. This is not a pathology to be engineered away; it is the steady-state condition of the network. The optimization literature acknowledges it plainly. The mixed-integer-linear-programming treatments of DSN scheduling describe the problem as oversubscribed, meaning that only a subset of the requested activities can be scheduled and network operators must decide which activities to exclude, and they calibrate their methods on real DSN demand data in which requests exceed capacity [\[33\]](#ref-33). The next-decade assessments of how DSN time competes across mission classes reach the same conclusion from the demand side, documenting that radio science, planetary radar, and the flagship mission portfolio increasingly contend for the same hours [\[22\]](#ref-22). Oversubscription, then, is the agreed premise. What the literature has not done, and what this dissertation does, is characterize the statistical shape of the penalty that oversubscription leaves behind after the schedulers have done their best.

A causal reading of why oversubscription persists and concentrates is worth stating now, because it organizes the whole argument and is developed formally in Chapter 2. The driver is that many missions each optimize locally: facing the prospect of being cut, a mission submits its requests early, pads the requested duration to hedge against shortening, and escalates priority for its critical phases. The mechanism by which these local optimizations produce a system-level pattern is looped, delayed feedback among the missions, operating through a shared schedule whose geometry imposes hard deadlines: a target is visible from a given complex only within a bounded window, so a request that is not served before its window closes is lost rather than merely delayed. The observable effect that this mechanism predicts is not a uniform thin spreading of small delays but a heavy upper tail of waits and losses bunched onto the windows where many missions' locally optimal requests collide. The operational consequence is that a small set of windows would carry a majority of the lost science return and of the degraded navigation tracking. The strategic implication is that the right remedy depends entirely on whether this prediction holds, which returns us to the research question. This causal chain is, at this stage, a theoretical expectation with moderate-to-high support from the structure of the system; whether the DSN logs realize it is the empirical question, and the confidence in the empirical claim is, deliberately, undetermined until the design is executed.

## 1.3 From "oversubscribed" to a measurable distributional question

The move that makes this dissertation more than a restatement of a known fact is the reframing of "the DSN is oversubscribed" as a precise, measurable, distributional question. Oversubscription, stated as such, is a qualitative condition; it tells a planner that demand exceeds supply but says nothing about how the resulting shortfall is distributed across requests, missions, geometries, and time. The aggregate satisfaction rate that the operational literature reports, the fraction of requested activities that are ultimately served, is a single number, and a single number is a mean. A mean is silent on the property that matters most for deciding what to do about the shortfall: whether the unserved and reduced requests are scattered thinly and evenly across the whole portfolio or are bunched onto a small number of structurally identifiable windows.

The distinction is not academic. Consider two networks with the same eighty-five-percent aggregate satisfaction rate. In the first, every mission, on every kind of request, in every geometry, loses fifteen percent of its requested time, more or less at random. In the second, most missions lose almost nothing most of the time, but a handful of recurring windows, conjunction-driven viewing overlaps, critical mission events, intervals of peak concurrency, absorb nearly all of the loss, so that within those windows the realized satisfaction rate collapses. The two networks are indistinguishable at the level of the mean and radically different at the level of the distribution. In the first, the only way to recover lost science is to add capacity broadly, because the loss is everywhere. In the second, the highest-return action is to identify the carrying windows and target them, because relieving a small number of windows recovers most of the lost science at a fraction of the cost of broad expansion. The reframing therefore converts an acknowledged operational fact into a question with a determinate, decision-relevant answer: what is the shape of the loss distribution, and is the loss concentrated.

Two statistical properties operationalize "shape." The first is the tail behavior of the relevant distributions, in particular the distribution of request-to-allocation wait time and the distribution of lost downlink. A light-tailed distribution, such as an exponential, has the property that extreme values are vanishingly rare and the mean is an adequate summary; a heavy-tailed distribution has the property that extreme values, though individually uncommon, are common enough and large enough to dominate the aggregate, so that the mean understates the true exposure. The second property is concentration: the degree to which the total lost downlink is carried by a small fraction of the structural windows. Concentration is measured by a Gini-type coefficient across windows and by the share of total loss carried by the top decile of windows. Under perfect uniformity, the top decile of windows carries ten percent of the loss; under strong concentration, it carries far more. Tail behavior and concentration are related but distinct: tail behavior is a property of the distribution of an outcome over requests, while concentration is a property of how an outcome aggregates over structural cells. The contribution of this dissertation requires evidence on both, and the acceptance rule, stated in the next section, demands that both pass before the alternative is accepted.

This reframing also identifies precisely where the existing scholarship stops. The DSN scheduling literature is strong on mechanism: it formulates the allocation as constraint satisfaction, mixed-integer linear programming, multi-objective optimization, reinforcement learning, and even quantum annealing, and it reports schedule-quality metrics such as the number of conflicts resolved or the fraction of requests satisfied [\[10\]](#ref-10). The capacity and traffic-forecasting literature is strong on aggregate loading and on the projection of future demand [\[17\]](#ref-17), [\[31\]](#ref-31). Between the two sits an unfilled gap: no published treatment asks the distributional question. The optimization literature produces better schedules and reports the residual as a mean; the forecasting literature projects the aggregate shortfall and reports it as a total. Neither decomposes the realized penalty into a distribution over requests or over windows. That decomposition is the contribution.

## 1.4 The single falsifiable contribution

The contribution of this dissertation is one falsifiable claim about the shape of the science-throughput penalty, stated as a pair of competing hypotheses preserved verbatim from the approved prospectus. The hypotheses are constructed so that each clause carries a pre-registered test with a pre-registered decision rule, which is what makes the contribution scientific rather than rhetorical: there is a concrete, achievable data outcome under which the contribution is refuted.

**H0 (null):** DSN scheduling friction is roughly uniform. Request-to-allocation wait times and pass-loss events are adequately described by a light-tailed (for example exponential or near-exponential) distribution, and no small subset of orbital-geometry, band, or mission-phase windows accounts for a disproportionate share of lost downlink. Under H0, a Gini-type concentration measure of lost downlink across windows is low, and the share of total loss carried by the top decile of windows is close to the ten percent that uniformity would predict.

**H1 (alternative):** DSN scheduling friction is heavy-tailed and concentrated. The wait-time distribution and the pass-loss distribution exhibit heavy tails that are better described by a power-law, log-normal, or generalized-Pareto upper tail than by an exponential, and a minority of identifiable geometry and phase windows (for example conjunction-driven viewing overlaps, critical mission events, and high-load concurrency intervals) account for a majority of the lost downlink.

The contribution is composite, and its acceptance rule is therefore strict. It comprises two clauses, a wait-time-tail clause and a concentration clause, and the alternative H1 is accepted only if *both* clauses pass their pre-registered tests; if either clause fails, the contribution is refuted and the null is retained for that clause. This conjunctive structure is a deliberate guard against the temptation to declare a partial victory. A heavy tail in waits without concentration of loss, or concentration of loss without a heavy tail in waits, would each be an interesting partial result but would not establish the claim as stated, and the design does not permit the claim to be rescued by relabeling a partial outcome as a success.

The claim is falsifiable in the strong sense because each clause has a quantitative decision rule fixed in advance. The wait-time-tail clause is tested by likelihood-ratio comparison of candidate heavy-tailed distributions against the exponential benchmark and by goodness-of-fit on the fitted upper tail, using the maximum-likelihood-plus-goodness-of-fit framework of Clauset, Shalizi, and Newman and its software implementations; a generalized-Pareto fit above a diagnostically chosen threshold supplies the formal tail estimator, in which a significantly positive shape parameter is the signature of a heavy tail. The concentration clause is tested by the share of total lost downlink carried by the top decile of windows against the ten-percent uniformity benchmark and by the Gini coefficient of loss across windows. If, on the full data, the wait-time tail is statistically indistinguishable from exponential and the top-decile loss share sits near ten percent, then H0 survives and the contribution is refuted. That this refutation is achievable, and would itself be reportable and useful, is what distinguishes a falsifiable contribution from an article of faith. The detailed estimators, decision thresholds, and goodness-of-fit procedures are specified in Chapters 5 and 6; here it suffices that the claim is one claim, that it is composite-but-conjunctive, and that it can be wrong.

The contribution's boundaries deserve a plain statement of what it is *not*. It is not a new DSN scheduling algorithm; the optimization literature is mature, and improving the schedule is not the object. It is not a capacity forecast; the traffic-modeling literature already projects aggregate demand. It is not a causal proof that the Forrester feedback mechanism produces the concentration; the cross-sectional design can test the convex load-response signature that the mechanism predicts but cannot, by itself, establish the feedback dynamics as the cause. The contribution is narrower and sharper than any of these: it is a measured characterization of the *shape* of the residual penalty, against a stated null, with a pre-registered way to be wrong.

## 1.5 Why it matters for NASA, JPL, and the named stakeholders

The reason the shape of the penalty matters, rather than only its average, is that NASA and JPL hold several distinct levers on the penalty and each lever costs money, and the optimal allocation of that money depends entirely on whether the penalty is uniform or concentrated. NASA invests in DSN aperture, in scheduling software, and in mission-side data-management policy; each of these is a lever, and each has a price. If the penalty is concentrated, a small targeted intervention aimed at the carrying windows can recover a large share of lost science, which is the highest-return use of a constrained aperture and operations budget. If the penalty is uniform, targeted interventions buy little and only broad capacity expansion helps. The distinction is not a refinement; it is a fork in the investment road, and the agency cannot currently tell which branch it is on because the only quantity it measures, the aggregate satisfaction rate, is blind to the difference.

The stakes are sharpest in the navigation-and-guidance category that is this dissertation's home. Lost downlink is ordinarily understood as lost science data, and that framing alone would justify the study. But the same contested aperture carries radiometric tracking, and a tracking pass lost or shortened in a navigation-critical phase, a trajectory-correction maneuver, an encounter, an entry-descent-and-landing sequence, degrades the orbit-determination solution at precisely the moment that solution governs a decision that cannot be retaken. The navigation stakes are therefore not a softer version of the science stakes; they are a harder one, because navigation errors propagate forward into the trajectory and can compound. If the loss is concentrated on critical-phase windows, as the mechanism in Section 1.2 predicts, then the concentration falls disproportionately on exactly the passes whose loss is most consequential for guidance. A characterization that localizes the carrying windows is thus directly useful to navigation planning, not only to data-return accounting, and the dissertation reports the penalty both in data-volume units and, where mission records permit, weighted by mission-declared criticality so that the navigation-critical losses are not averaged into invisibility.

The named beneficiaries are concrete. NASA's Space Communications and Navigation program and its systems-engineering office commission the periodic JPL traffic studies precisely to inform strategic and programmatic decisions about how the DSN should evolve [\[31\]](#ref-31); a distributional characterization of the penalty gives those decisions a target rather than an average. JPL, as the institution that operates the DSN and develops its scheduling systems, gains a way to evaluate whether a proposed scheduling-policy change or a proposed demand-access capability would relieve the windows that actually carry the loss. The NORTH STAR navigation-and-guidance planning context gains the orbit-determination-relevant reading: which mission phases, in which geometries, are losing the tracking that their navigation solutions depend on. Even a refutation serves these stakeholders, because a credible finding that the penalty is uniform would justify broad capacity expansion and would retire the hypothesis that targeted intervention is the higher-return path. The value of the work to its stakeholders is, in both outcomes, the conversion of a known shortfall into a measured quantity that an investment decision can act on.
## 1.6 Scope, delimitations, and the design-stage guardrail

The scope of this dissertation is deliberately bounded, and stating the boundaries protects the claim from being read as larger than it is. The work is a design-stage analysis plan. It specifies the data, the units of analysis, the variables, the estimators, the identification strategy, the pre-registered tests, and the decision rules required to answer the distributional question, and it argues from the structure of the system and from analogous systems what the answer is likely to be. It does not execute the estimation on the DSN logs. This is the central delimitation, and it is enforced throughout: no empirical result is claimed as having been computed, and every magnitude that appears in the expected-findings discussion of the later chapters is labeled as an illustrative placeholder chosen to show the *form* a result would take, never as an estimate. The guardrail is not a disclaimer appended for caution. It is a substantive condition on every empirical sentence in the document, and the reader is entitled to treat any unlabeled empirical number as an error.

Several further delimitations bound the scope. First, the study is confined to the DSN as the shared asset; it does not address near-Earth tracking networks or commercial ground-station services except as analogues in the literature review. Second, within the DSN, the primary outcome is the science-throughput penalty operationalized as lost downlink and as request-to-allocation wait, with radiometric-tracking degradation treated through the criticality weighting rather than through an independent orbit-determination error model; a full propagation of lost tracking into navigation covariance is acknowledged as valuable and is placed outside the boundary of this design. Third, the contribution is a characterization of shape, not a causal identification of the feedback dynamics; the convex load-response curve is tested as the mechanism's signature, but the cross-sectional design's inability to prove the feedback causation is stated as the boundary of the claim rather than papered over. Fourth, the external-validity reach is limited to the studied mission mix; the crewed-exploration era will shift the mix toward high-rate time-critical traffic that the historical logs cannot contain, so claims about that era are made only through the reported load-response curve and not through a point estimate.

The architecture-traceability layer that a system-or-capability dissertation would carry is explicitly out of scope here, and the reason is recorded so that its absence is not mistaken for an omission. This dissertation is a statistical and operations-research analysis plan about the distributional shape of a scheduling penalty; it does not design, specify, or field a capability, a system function, or a data-or-service exchange. Forcing enterprise-architecture vocabulary, a strategic-objective-to-capability-to-activity-to-function-to-exchange chain, onto a queueing study would be placeholder formalism with no referent. The decision-relevance of the work is captured instead through the named causal mechanism and through the lever analysis in the discussion chapter, which map the research objective to a concrete planning decision, capacity versus policy versus demand-shaping, without an architecture layer. The omission is therefore principled and deliberate, consistent with the rule that an architecture-traceability chain should be populated only when the work genuinely concerns a real system, capability, or exchange.

## 1.7 Definitions of key terms

The argument depends on a small set of constructs used with fixed meanings throughout the dissertation. They are defined here and used identically in every subsequent chapter.

The **tracking-pass request** is the primary unit of analysis: one requested tracking activity, for one mission, on one antenna class, over one viewing window. It is the row of the analytical panel, the subject of the survival model, and the unit over which pass-loss is defined.

The **geometry-phase window** is the secondary unit of analysis: a discretized cell defined by the cross-classification of an orbital-geometry condition, a mission phase, a complex, and a band. Lost downlink is aggregated to these windows, and the concentration tests operate over them.

**Wait time**, denoted W, is the elapsed time from the submission of a request to its confirmed allocation. It is right-censored for requests that remain pending at the observation cutoff or whose viewing window expires before allocation, which makes it time-to-event data and dictates the survival-analytic treatment.

The **pass-loss indicator**, denoted L, is binary: it equals one when a requested pass is dropped, expires unserved, or is reduced below a science-useful threshold, and zero when the pass is executed as requested. The science-usefulness threshold that distinguishes a reduced-but-useful pass from a lost one is a modeling choice that is varied in sensitivity analysis rather than fixed by fiat.

The **lost-downlink magnitude**, denoted D, is the shortfall between the requested data return and the executed data return for a lost or reduced pass, expressed in physical bit-volume units and computed from band, requested duration, and the mission's nominal data rate. D is the science-throughput penalty in physical units and may be additionally weighted by mission-declared criticality so that navigation-critical losses are not averaged away. When aggregated to a geometry-phase window w, the per-window loss is written \(D_w\).

The **covariates**, denoted X, are the structural conditions hypothesized to drive loss: orbital-geometry measures (target declination, viewing-window overlap among concurrently supported targets, elevation profile at each complex, and conjunction or occultation compression of the usable window); frequency band (for example S, X, Ka), which governs antenna eligibility and band-specific contention; concurrent-mission load (the count and aggregate requested antenna-time of other missions contending for the same complex and band in the same interval), which operationalizes the inflow-shape variable; and the mission-phase indicator (launch, maneuver, encounter, entry-descent-landing versus cruise).

For the formal models, the **allocation hazard** is written \(h(t \mid X)\) with the Cox proportional-hazards form \(h(t \mid X) = h_0(t) \exp(\beta^\top X)\), and the Kaplan-Meier survival function of the wait is written \(S(t)\). The candidate **heavy-tail families** are the exponential (the light-tailed null benchmark), the log-normal, the power-law with exponent \(\alpha\), and the generalized Pareto with scale \(\sigma\) and shape \(\xi\), where \(\xi > 0\) is the formal heavy-tail signature. **Concentration** is summarized by the Gini coefficient G of \(D_w\) across windows and by \(T_{10}\), the share of total loss carried by the top decile of windows. The **fixed effects** are the mission fixed effect \(\mu_m\) and the epoch fixed effect \(\lambda_t\), which absorb time-invariant mission characteristics and network-wide period shocks respectively. These definitions and this notation are fixed; the later chapters extend them but never redefine them.

## 1.8 Roadmap of the dissertation

The remaining chapters build the case for, and the means of testing, the single contribution. The structure follows the logic of the argument: the problem is real, the problem is material, the proposed analysis addresses the causal mechanism, it beats the alternatives, and its residual risk is acceptable.

**Chapter 2, the theoretical framework**, supplies the three lenses that together make the heavy-tail-and-concentration hypothesis a structured prediction rather than a guess. The queueing lens models the DSN as arrivals contending for servers under deadline-driven loss and identifies three distinct routes, hard viewing-window deadlines, bursty clustered arrivals, and skewed service requirements, by which a moderately loaded queue develops a heavy upper tail of waits. Jay Forrester's system dynamics supplies the structural reason concentration is plausible: backlog and unmet-requirement stocks, request and service flows, and delayed feedback among locally optimizing missions that piles contention onto shared windows. Nassim Taleb's program supplies the statistical discipline: test for fat tails rather than assume them away, and read a convex load-response as the signature of fragility. The chapter ends by integrating the three into the single named causal mechanism that the design is built to test.

**Chapter 3, the literature review**, positions the contribution in the scholarly record. It surveys DSN scheduling as optimization across constraint satisfaction, mixed-integer programming, evolutionary methods, reinforcement learning, and quantum annealing, and shows what that literature does not do, namely characterize the residual penalty's distribution. It reviews DSN capacity and traffic forecasting and the broader ground-station and constellation contact-scheduling literature, and it locates the gap, optimization reports a mean while no treatment reports a distribution, as the hinge into which this dissertation fits.

**Chapter 4, data and measurement**, names the three data sources, the DSN scheduling and tracking logs accessed through the service catalog and Service Preparation Subsystem archives, the NTRS DSN loading and forecasting reports, and the mission downlink-requirement records, and converts each operational record into the measured constructs defined above. It states plainly that requested time is a hedged quantity rather than clean demand, sets the multi-year coverage requirement needed to observe the tail, and enumerates the measurement limitations, while reaffirming that no logs have yet been analyzed.

**Chapter 5, the research design**, fixes the three estimands (wait-time shape, loss shape and concentration, and conditional pass-loss drivers), matches each to an estimator (Kaplan-Meier and Cox proportional hazards for the survival analysis, heavy-tail distribution fitting for the shape, and logistic and skewed-GLM regression for the drivers), and lays out the identification strategy built on within-mission and within-epoch variation with mission and epoch fixed effects and a geometry-driven, behavior-free robustness instrument. It closes with the threats-to-validity analysis across internal, external, construct, and statistical-conclusion validity.

**Chapter 6, the analysis plan**, specifies the five pre-registered estimation steps, the heavy-tail fitting protocol, the concentration metrics, and the decision rules, and it presents the expected findings in the illustrative-placeholder form the guardrail requires, every magnitude labeled as such, while stating what a robust positive or negative result would and would not establish.

**Chapter 7, the discussion**, draws the implications: under a concentration result, three levers, capacity and arraying, scheduling policy, and demand shaping, keyed to the carrying windows; the rival explanations and how the design addresses each; the external-validity reading through the load-response curve for the exploration era; and the relationship to alternative supply levers such as deep-space optical communications and antenna arraying [\[67\]](#ref-67).

**Chapter 8, the conclusion**, restates the falsifiable contribution and the reframing from a known fact to a measurable distributional question, separates what is established from what is left open at design stage, and develops the argument that both outcomes are useful, refutation justifying broad capacity expansion and confirmation justifying targeted intervention, before closing on the decision relevance for NORTH STAR navigation-and-guidance planning and the future work that an executed study would open.

Taken together, the chapters carry one argument from premise to test. The premise, established in this introduction and grounded in the institutional and historical record, is that the DSN is structurally and durably oversubscribed and that the residual penalty is currently visible only as a mean. The reframing is that the penalty has a shape, tail behavior and concentration, that the mean conceals and that determines the right remedy. The contribution is the falsifiable claim that the shape is heavy-tailed and concentrated, against the uniform null, with a pre-registered way to be wrong. The mechanism that makes the claim structured is queueing-plus-Forrester-plus-Taleb. The honesty condition, carried on every empirical sentence, is that this is a design, not a set of results. The remaining chapters supply the framework, the literature positioning, the data, the design, the analysis plan, the discussion, and the conclusion that turn that claim into something an examiner can evaluate and an executed study could decide.


# Chapter 2: Theoretical Framework

## 2.0 The chapter's answer, stated first
One thesis organizes the argument that follows: the science-throughput penalty the Deep Space Network (DSN) imposes through antenna-scheduling contention is, on theoretical grounds, more likely to be heavy-tailed and concentrated than uniform, and the burden of proof therefore belongs on the light-tailed null rather than on the heavy-tailed alternative. The argument is not that H1 is true. No estimation has run, and the design is built precisely so that H0 remains a live, reportable outcome. The argument is narrower and prior to estimation: three independent bodies of theory, each mature and each anchored in primary literature, converge on the same structural prediction, so a competent prior places more weight on concentration than a naive congestion picture would. Queueing theory supplies the formal model of waits and deadline-driven losses and identifies the mechanisms by which a moderately loaded server develops a heavy upper tail of waits. Jay Forrester's system dynamics supplies the structural reason that contention should pile onto a minority of shared windows rather than smear evenly across the calendar. Nassim Taleb's program on fat tails supplies the statistical discipline that converts the first two into a testable, falsifiable claim and warns against the asymmetric cost of assuming thin tails by default.

Four moves clarify what is at stake. The current state of DSN analysis treats the residual penalty after optimization as an aggregate satisfaction rate, a mean. The desired state is a characterization of the distributional shape of that penalty, its tail behavior and its concentration, grounded in the structure of the system rather than in a convenient assumption. The gap is that the operational and the optimization literatures, strong as they are on mechanism and on aggregate loading, never ask the distributional question, and a mean conceals whether the unserved requests are scattered thinly or bunched onto identifiable geometry and phase windows. The consequence of leaving the gap open is that theory underdetermines the remedy: without knowing the shape, a planner cannot tell whether broad capacity expansion or targeted intervention recovers the most science return, and the two cases imply opposite spending. The theoretical half of that gap closes here. Drawing on primary sources, the conceptual model developed in the sections that follow predicts which case holds and specifies how each framework transfers to the DSN problem, so that Chapters 4 through 6 can put the prediction to a pre-registered empirical test.

The confidence posture is fixed for the whole chapter and is design-stage by construction. The *mechanism* for H1 is well-supported in theory, at high confidence, because it rests on three converging and independently established literatures. Whether the mechanism actually operates at material magnitude on the real DSN logs is *untested*, and is stated as such everywhere. The correct reading of every claim below is therefore "the framework predicts X; whether the data show X is the empirical question this design exists to answer."


## 2.1 The queueing lens: arrivals, servers, deadlines, and the tail of the wait

### 2.1.1 The framework and its primary sources

Treating a contested allocation system as a queue is standard operations-research practice, and the vocabulary is settled. A queue is specified by its arrival process, its service-time distribution, the number of servers, the queue capacity, and the service discipline, summarized in Kendall's notation, whose embedded-Markov-chain analysis of queues with general service distributions is the founding formal treatment [\[8\]](#ref-8). Kleinrock's standard reference supplies the results that matter here: the waiting-time distribution and its tail behavior under various arrival and service regimes [\[7\]](#ref-7). The single most important fact that the queueing literature contributes to this dissertation is negative and counter to intuition. Queueing systems do not generally produce light-tailed waiting times. A system can be only moderately loaded on average and still generate a heavy upper tail of waits, because the tail is driven by the *structure* of arrivals, service, and discipline, not by the mean load alone.

That fact is not folklore; it is theorem. Takahashi proves that in a multiserver queue with phase-type interarrival and service distributions the waiting-time tail is asymptotically exponential with a decay parameter determined by the transforms of the input distributions, which establishes the light-tailed baseline against which heavier behavior is measured [\[46\]](#ref-46). Asmussen and O'Cinneide then show that when the arrival or service process is *modulated*, that is, when its parameters themselves vary over a background state, the exponential decay parameter of the wait is no larger than that of the corresponding queue with averaged parameters, with a sharp condition for when the two coincide [\[80\]](#ref-80). The practical reading is direct: averaging the load away cannot make the tail lighter and generally makes it heavier, so a satisfaction rate computed on averaged load *understates* the tail it is meant to summarize. The heavy-traffic literature reinforces the point from the opposite limit. Gamarnik and Stolyar characterize the stationary queue in the Halfin-Whitt regime, where utilization approaches one as the server pool grows, and bound the steady-state backlog under any non-idling discipline [\[43\]](#ref-43); Atar, Mandelbaum, and Reiman analyze scheduling of a multiclass queue with many servers and impatient customers in the same regime [\[45\]](#ref-45). Both establish that as a system is pushed toward full utilization, which is the chronic condition of the DSN, the wait distribution stops behaving like its average and the discipline's treatment of customer classes begins to dominate the realized waits.

### 2.1.2 How the framework transfers to the DSN

The mapping is exact rather than analogical. The DSN request stream is the arrival process: each mission's submission of a requested tracking activity is an arrival. The antennas are the servers, a bounded set of large-aperture dishes distributed across three complexes. A request that cannot be served immediately waits, which is the wait time \(W_i\), the elapsed time from submission to confirmed allocation, right-censored when a request is still pending or when its window expires before service. A request whose viewing window passes before it is served is *lost*, which the queueing literature names customer abandonment or deadline expiry, and which the dissertation operationalizes as the pass-loss indicator \(L_i\). The DSN schedule is not first-come-first-served; it is a priority-and-preference discipline negotiated among missions through a multi-stage process that runs from long-range forecasting through mid-range negotiation to near-real-time conflict resolution [\[10\]](#ref-10), [\[16\]](#ref-16). That structure, a negotiated priority discipline operating at near-full utilization with hard deadlines, is the structure the queueing theorems above identify as the one that converts moderate average load into a heavy upper tail of waits for the systematically deferred subclass.

Terekhov, Tran, Down, and Beck make the bridge between queueing and scheduling explicit, studying dynamic scheduling problems in which the choice of queue discipline shapes the realized wait distribution [\[9\]](#ref-9). Their result is the formal reason to treat the DSN schedule, an engineered discipline, as the object that determines the tail rather than as a neutral allocator. The expectation that follows can therefore be stated precisely. The DSN wait-time distribution should be expected, on queueing-theoretic grounds, to have an upper tail heavier than the exponential null, because the system runs near full utilization under a negotiated priority discipline with hard deadlines and modulated, class-dependent arrivals and service. Established queueing results carry the inference: modulation cannot lighten the tail [\[80\]](#ref-80), priority disciplines systematically defer a subclass whose waits then dominate the tail [\[9\]](#ref-9), and near-full utilization makes the discipline's class treatment govern the waits [\[43\]](#ref-43), [\[45\]](#ref-45). The phase-type baseline [\[46\]](#ref-46) fixes the exponential reference, so "heavier than exponential" is a well-defined comparison rather than a vague gesture. The expectation is exactly that, expected and not demonstrated; the magnitude is an empirical question. The obvious objection is that if the realized arrivals and service on the DSN are in fact near-Poisson and near-exponential with a discipline that does not persistently defer any subclass, the tail could be exponential and H0 would survive for waits, which is exactly the null the design is built to be able to accept.

### 2.1.3 Locating the DSN in the queue taxonomy, and why the location matters

Precision about where the DSN sits in the Kendall taxonomy matters, because the location is what licenses the heavy-tail expectation rather than a generic appeal to congestion. In the A/B/c/K/discipline shorthand, the arrival process A is not Poisson: it is geometry-clustered and, as Section 2.2.2 argues, plausibly self-similar, so the memoryless assumption that would deliver clean light-tailed results is violated at the input. The service distribution B is not a single exponential: it is a heavy-skewed mixture of short routine cruise passes and long, rigid critical-event passes, so the M/M abstraction that produces the tidiest tail results does not apply. The server count c is small, fixed, and partitioned by band and complex, so the smoothing that a large homogeneous server pool would provide is absent precisely where it would help; the antennas are not interchangeable, since a Ka-band request cannot be served by an S-band-only aperture, which fragments the effective server pool into smaller, more easily overwhelmed sub-pools. The buffer K is effectively zero in the deadline sense, because a request that is not served within its viewing window leaves the system unserved rather than waiting indefinitely. And the discipline is neither first-come-first-served nor a simple priority rule but a negotiated, preference-weighted, multi-stage allocation. Every one of these five coordinates moves the DSN away from the regime in which light tails are guaranteed and toward the regime in which the queueing theorems of Section 2.1.1 predict heavy ones. The location in the taxonomy is therefore not incidental: it is the structural reason the dissertation treats the exponential as a null to be tested rather than a property to be assumed. The interpretive weight of this subsection is that the heavy-tail prediction does not rest on any single exotic feature of the DSN; it rests on the *conjunction* of five ordinary-looking departures from the textbook M/M/c queue, each of which is independently documented in the operational literature [\[10\]](#ref-10), [\[16\]](#ref-16), [\[35\]](#ref-35), and each of which pushes in the same direction.


## 2.2 Three DSN-specific routes to a heavy tail

Section 2.1 establishes that queues *can* produce heavy tails. This section names the three specific, independent mechanisms by which the DSN in particular is structured to do so. The purpose is to make the H1 prediction concrete rather than speculative: each route is a known heavy-tail mechanism in the queueing literature, and all three are present in the DSN by construction, not by coincidence. When three independent routes to the same destination are all open, the burden of proof properly sits on the party claiming the destination is not reached.

### 2.2.1 Route one: hard viewing-window deadlines and abandonment

A deep-space target is visible from a given complex only for a bounded interval set by celestial mechanics. A request not served before its window closes is not merely delayed; it is lost. This is deadline-driven abandonment, and the queueing literature on impatient customers is the relevant primary source. Boots and Tijms give the loss probability for a multiserver queue with impatient customers and general service, exact for exponential service and an excellent heuristic otherwise [\[48\]](#ref-48). Gromoll, Robert, and Zwart, and the related processor-sharing analysis with Bakker, develop fluid limits for queues with reneging and show that impatience materially reshapes the steady state relative to the patient case, including a non-trivial defected mass and altered conditional waits among survivors [\[49\]](#ref-49), [\[95\]](#ref-95). Huang and Zhang extend the diffusion approximation to networks with reneging under heavy traffic, confirming that the abandonment process has its own limit behavior distinct from the queue-length process [\[84\]](#ref-84). The mechanism that matters is this: under a deadline-with-abandonment discipline, the requests that survive to be served late are not a random sample of all requests; they are the ones the discipline could afford to defer. The wait distribution among survivors therefore develops a heavy conditional tail, and the loss process concentrates on the requests whose deadlines the discipline chose to let expire. Earliest-deadline-first and shortest-remaining-processing-time disciplines, which are close analogues of the deadline-aware negotiation the DSN performs, have been analyzed in heavy traffic and shown to admit heavy-tailed inputs while transforming them in discipline-specific ways [\[85\]](#ref-85). Transfer to the DSN: the viewing window is the deadline, \(L_i\) is the abandonment indicator, and the prediction is that loss is not spread uniformly across requests but concentrates on the deadline-binding ones, which are the conjunction-driven and critical-event windows.

### 2.2.2 Route two: bursty, clustered, self-similar arrivals

The DSN arrival process is not smooth. Requests cluster on the geometry windows when many targets are simultaneously well placed, so the instantaneous offered load far exceeds the average during those intervals. Burstiness in the arrival process is one of the classical routes by which an otherwise moderately loaded queue develops heavy waiting-time tails. The foundational evidence is Leland, Taqqu, Willinger, and Wilson's demonstration that aggregate network traffic is statistically self-similar, with no natural burst length and burstiness that *intensifies* rather than smooths under aggregation, a finding that overturned the Poisson modeling assumption for such systems [\[51\]](#ref-51). Liebeherr, Burchard, and Ciucu derive delay bounds for networks carrying heavy-tailed and self-similar traffic, giving the formal link from self-similar input to heavy-tailed delay [\[52\]](#ref-52). Barabasi's account of priority queues closes the loop on the *origin* of the burstiness: Vazquez and colleagues, and Blanchard and Hongler, show that when a single server executes tasks by perceived priority, the waiting-time distribution is heavy-tailed by construction, with most tasks served fast and a few waiting nearly forever, and that this holds even when arrivals are not themselves bursty [\[83\]](#ref-83), [\[82\]](#ref-82). The DSN combines both sources: geometry clusters the arrivals, and the priority discipline frozen-prioritizes a low-priority subclass. Transfer: the concurrent-mission load covariate \(X\) operationalizes the instantaneous burst, and the prediction is that waits incurred during burst intervals populate the upper tail.

### 2.2.3 Route three: skewed, heterogeneous service requirements

The third route is the service-time distribution itself. A high-rate critical-event pass occupies an antenna far longer and far more rigidly than a routine cruise pass, so the service requirement is heavy-skewed across request types, and skewed service is the third classical route to heavy waits. Aalto and Ayesta analyze optimal scheduling for jobs with a decreasing-hazard-rate (heavy) service tail and show how the discipline interacts with the service tail to determine mean delay [\[81\]](#ref-81). Bladt and Rojas-Nandayapa show that such heavy-tailed service distributions can be densely approximated by phase-type scale mixtures, which is the technical route by which heavy service requirements are fit and propagated through the wait [\[59\]](#ref-59). The point is not that any single route must dominate. It is that all three, deadline abandonment, bursty arrivals, and skewed service, are present in the DSN simultaneously and by construction. Each alone is a known sufficient condition for a heavy wait tail; together they make the light-tailed null the implausible default. This is the queueing-theoretic reason the dissertation *tests for*, rather than assumes away, the fat tail, and it is the established basis for placing the burden of proof on H0.


## 2.3 Forrester's lens: stocks, flows, delayed feedback, and structural concentration

### 2.3.1 The framework and its primary sources

Queueing theory explains how the DSN can produce a heavy tail. Jay Forrester's system dynamics explains why the loss should *concentrate* on a minority of windows rather than spread, and it does so at the level of system structure rather than statistics. Forrester's founding statement holds that the behavior of a complex system is governed by its stocks (accumulations), its flows (the rates that fill and drain those stocks), and the information feedback among them, which operates with delay [\[21\]](#ref-21). His central and deliberately counterintuitive claim, developed across the system-dynamics program, is that system behavior is dominated by loop structure and delay, not by the intentions of the actors, and that this routinely produces outcomes that no actor wants and that local reasoning cannot anticipate [\[23\]](#ref-23), [\[24\]](#ref-24). Two strands of the modern literature sharpen the transfer. Sweeney and Sterman's bathtub experiments show empirically that even highly educated subjects fail to infer accumulation behavior from flows, which is the cognitive reason backlog stocks must be modeled formally rather than reasoned about informally [\[25\]](#ref-25). Croson, Donohue, Katok, and Sterman demonstrate in controlled supply-chain experiments that locally rational ordering, under coordination risk and delay, amplifies into the bullwhip oscillation upstream, and that a coordination stock dampens it [\[63\]](#ref-63). Sterman, Oliva, Linderman, and Bendoly survey the application of exactly this apparatus to operations management, establishing that feedback, delay, and accumulation are the standard lens for operational systems with the DSN's structure [\[62\]](#ref-62).
### 2.3.2 How the framework transfers to the DSN

In Forrester's terms the state of the DSN allocation system lives in stocks: the backlog of unserved or partially served requests, and the accumulated unmet-downlink requirement carried by each mission. These stocks change through flows: the arrival rate of new requests and the service rate at which passes are allocated and executed. The two are coupled through information feedback with delay. When backlog rises, missions respond, each rationally from its own vantage, by submitting requests earlier to secure a place, by inflating requested durations to hedge against being cut, and by escalating priority for critical phases. Each response is a balancing action locally; in aggregate the responses are a reinforcing pressure on contention during the windows everyone wants. This is the bullwhip structure of [\[63\]](#ref-63) transposed onto a scheduling system: local hedging under delay amplifies into systemic concentration. Forrester's deeper claim supplies the *causal* prediction. Because the relieving feedback (a mission learning that a window is over-contended and relaxing its request) operates with a delay longer than the window itself, the system cannot self-correct within the window, and contention does not smear evenly across the calendar; it piles onto the geometry and phase windows where many missions' local optimizations collide.

The named causal mechanism, which the chapter builds toward and on which the rest of the argument depends, is as follows:

```
Driver:        Many missions locally optimize (submit early, pad requested durations,
               escalate priority for critical phases)
  -> Mechanism: Looped, delayed feedback (Forrester) piles those locally optimal requests
                onto the SAME shared geometry/phase windows, while deadline-driven viewing
                geometry (hard window close), bursty arrivals, and skewed service requirements
                (the three queueing routes of 2.2) convert moderate average load into a heavy
                upper tail of waits for the deferred subclass
  -> Observable effect: heavy-tailed wait-time and pass-loss distributions; lost downlink
                concentrated on a minority of windows; convex (accelerating) lost-downlink-
                vs-load curve (the Taleb fragility signature of 2.4)
  -> Operational consequence: a small set of windows carries a majority of lost science return
                and degraded orbit-determination tracking
  -> Strategic implication: targeted aperture/policy/demand-shaping at the carrying windows
                recovers the most science per dollar; the exploration-era penalty scales
                worse-than-linearly, so planning must use the load-response curve, not the average
```

This is a causal claim with a named mechanism, not a bare correlation. The driver is local optimization by missions; the mechanism is delayed feedback piling requests onto shared windows compounded by the three queueing routes; the observable effect is heavy tails and concentration; the operational consequence is carrying windows; the strategic implication is targeted remedy. Where the design can only establish correlation rather than the full causal chain, Section 2.4 and Chapter 6 say so explicitly and downgrade confidence accordingly: the cross-sectional design tests the *signature* of the mechanism (a convex load-response) but does not, by itself, prove the Forrester feedback loop generated it. That boundary is stated plainly and is the limit of the causal claim.

The system-dynamics method is not merely metaphorical here; it is an instrumented, reusable modeling tradition. Its application to aerospace and defense programs, where component-delay feedback cascades into project disruption, is documented [\[90\]](#ref-90), and the same stock-and-flow apparatus has been operationalized as running software in an adjacent space-systems domain, where object populations are stocks driven by launch, decay, and removal flows [\[30\]](#ref-30). The DSN backlog-and-unmet-requirement stock, driven by request and service flows under delayed feedback, is the same kind of object, which is why the structural prediction of concentration transfers an established method rather than proposing a novel and untested analogy.

### 2.3.3 The inflow-shape corollary

Forrester's tradition yields a sharp secondary prediction directly relevant to the dissertation's covariates: the *temporal shape* of an inflow, not merely its total, determines whether a stock stabilizes or runs away. The same inflow-shape logic has been applied in a space-systems setting, where the distribution of launch *timing*, not the average launch rate, governs whether the orbital-object stock stabilizes or grows unstably [\[19\]](#ref-19), with the broader stock-and-flow population-dynamics framing of that domain establishing the method [\[20\]](#ref-20). Transferred to the DSN, this says the penalty should be driven by the *distribution of request timing* relative to the geometry windows, not by the average load. That is the structural justification for making concurrent-mission load and viewing-window overlap the central covariates \(X\) rather than relying on a single aggregate load figure. The corollary is testable: if the average load explained the loss, H0 would be favored; if the timing distribution explains it, H1 is favored.

### 2.3.4 What the structural reading does and does not support

The Forrester lens must be applied with discipline about the strength of the inference it supports, and this subsection draws the line explicitly so that later chapters do not overclaim. What the system-dynamics reading supports at high confidence is a *structural plausibility* argument: given backlog and unmet-requirement stocks coupled to request and service flows through feedback that is slower than the windows it would relieve, concentration is the expected behavior of the loop, not an anomaly requiring special explanation. This is a strong prior, and it is independently corroborated by the demonstrated bullwhip amplification of locally rational ordering under delay in controlled experiments [\[63\]](#ref-63) and by the documented cascade of component-delay feedback in aerospace programs [\[90\]](#ref-90). What the lens does *not* support is a claim that the dissertation has demonstrated the loop empirically. The design is cross-sectional over the realized logs; it can detect the *signature* the loop predicts, namely a convex load-response and concentrated loss, but it cannot trace the feedback edges themselves or rule out that some other generative process produced the same signature. The honest causal status is therefore this: mechanism specified and theoretically supported at high confidence, mechanism *operation on the DSN* inferred only through its signature and held at the design-stage confidence the whole dissertation maintains. This is also where the lens connects to the remedy logic developed in the discussion chapter. If concentration is loop-generated, then interventions aimed at loop structure, at the rules and feedback that govern how missions hedge and escalate, sit higher on the leverage ladder than interventions aimed at parameters such as raw aperture count, because changing the parameter leaves the loop that generates the concentration intact. That leverage ranking is the conceptual reason the discussion treats demand-shaping and scheduling-discipline policy as potentially higher-return than capacity alone, and it transfers directly the system-dynamics principle that the strongest intervention points are structural, not parametric. The interpretation to carry forward is that the framework does double duty: it predicts the *shape* the empirical chapters will test, and it ranks the *remedies* the discussion will weigh, and both follow from the same stock-flow-feedback reading.


## 2.4 Taleb's lens: Mediocristan versus Extremistan, and the discipline of not assuming thin tails

### 2.4.1 The framework and its primary sources

Forrester explains why concentration is structurally plausible. Nassim Taleb's program supplies the statistical discipline that turns plausibility into a falsifiable test and the risk reading that explains why getting the tail right is not a technicality. Taleb's organizing distinction is between two statistical regimes. In one, which his program labels the thin-tailed or Mediocristan regime, the mean and variance of a process are stable and no single observation can dominate the aggregate, so the average is an adequate summary and the historical record represents the process faithfully. In the other, the fat-tailed or Extremistan regime, a few extreme realizations dominate the mean, the variance may be effectively unbounded, and the historical record systematically undersamples the tail because the worst event has, by definition, not yet occurred. This is exactly the distinction at issue between H0 and H1. The methodological core of Taleb's relevant work is twofold and is adopted directly. First, the non-naive precautionary argument inverts the burden of proof: when a process *could* be fat-tailed and the downside is consequential, one must not assume thin tails by default, because the cost of falsely assuming thin tails is asymmetric and potentially unbounded [\[27\]](#ref-27). Second, the right object of study is the system's *second-order response* to a dose of the stressor, not a forecast of the stressor: fragility is formally a concave (and antifragility a convex) response of the outcome to variability in the input, detectable through the curvature of the response [\[28\]](#ref-28), [\[29\]](#ref-29).

### 2.4.2 How the framework transfers to the DSN

The transfer is direct and governs the dissertation's whole epistemic stance. If DSN wait-time and pass-loss live in Mediocristan, the aggregate satisfaction rate is an adequate summary, the worst windows are no worse than a scaled average, and uniform remedies follow; H0 holds. If they live in Extremistan, the mean is misleading, the sample undersamples the worst windows, any plan that uses the average loss understates the true exposure during the critical windows, and targeted remedies follow; H1 holds. Taleb's first instruction, do not assume light tails, is the methodological principle behind the entire research design: it is why the analysis fits the exponential as a *null to be rejected* rather than as a maintained assumption, and why the heavy-tailed candidates are given a fair test. That instruction is implemented through the Clauset-Shalizi-Newman maximum-likelihood-plus-goodness-of-fit procedure for distinguishing power-law and other heavy-tailed behavior from light-tailed alternatives in empirical data [\[4\]](#ref-4), with its standard software realizations in Python and R [\[5\]](#ref-5), [\[6\]](#ref-6), and the extreme-value peaks-over-threshold machinery for the upper tail specifically. The burden-of-proof inversion of [\[27\]](#ref-27) is the reason the design is honest about its own prior: it does not presuppose H1, but it does refuse to presuppose H0, and it pre-registers the decision rule so that the prior cannot quietly determine the conclusion.

Taleb's second instruction, study the convex response rather than forecast the stressor, supplies the dissertation's most distinctive empirical object. The relevant question is not when the next high-contention window will occur, which is a forecasting problem the design does not attempt, but how the lost-downlink response curves as concurrent load rises. A convex (accelerating) response is the signature of fragility: it means that a unit increase in load near the top of the load range costs disproportionately more lost downlink than the same increase near the bottom, which is the operational meaning of a fat tail in the loss process [\[28\]](#ref-28), [\[29\]](#ref-29). This is a falsifiable prediction with a clean null: if the load-response curve is linear or concave, the fragility signature is absent and H0 is favored on that clause; if it is convex, H1 is favored. The convexity reading has been applied to large project-cost distributions, where "regression to the tail" identifies strong convexity, fixed deadlines, and tight coupling as the generative drivers of a power-law cost distribution [\[61\]](#ref-61), and the convexity-and-fragility apparatus has been developed for managing downside risk in financial portfolios [\[60\]](#ref-60). The DSN shares the generative drivers, fixed deadlines and tight coupling among missions, which is the cross-domain basis for expecting the same convex signature.

### 2.4.3 A calibrated confidence statement

Taleb's framework also disciplines the confidence with which the prediction is stated, and the calibration is explicit. The *theoretical* support for the fragility prediction is high: three drivers (the queueing routes), a structural mechanism (Forrester feedback), and a cross-domain precedent for the convex signature (project costs) all point the same way. The *empirical* support is, at the design stage, absent, because no estimation has run; this is stated, not hedged. The evidence that would *raise* confidence in H1 is concrete: a likelihood-ratio test that prefers a heavy-tailed model over the exponential, a generalized-Pareto shape parameter \(\xi\) significantly greater than zero, a top-decile window share \(T_{10}\) materially above the ten-percent uniformity benchmark, and a measured convex load-response. What would *lower* it, toward H0, is equally concrete: a wait tail statistically indistinguishable from exponential, a \(T_{10}\) near ten percent, and a linear or concave load-response. The design grades its modality to this evidence: it asserts the *mechanism* with high confidence and the *empirical realization* of the mechanism as an open question, never conflating the two. This is the Taleb discipline applied reflexively to the dissertation's own claims, and it is the reason the contribution is scientific rather than rhetorical.

### 2.4.4 Why the convex response is the operationally decisive object

One implication of the Taleb lens deserves separate development because it is the hinge between the theoretical model and the dissertation's claimed value to NASA and JPL. A planner facing a growing mission portfolio does not, in practice, need a forecast of which specific window will be the next to overload; that forecast is fragile and, in the Extremistan case, effectively impossible because the worst window is undersampled in the historical record by construction. What the planner needs is the *response function*: how does expected lost downlink move as concurrent load rises? If that function is linear, the system is in Mediocristan with respect to load, the average loss scales predictably, and a satisfaction rate extrapolates honestly into the higher-load future. If the function is convex, the system is fragile to load, the marginal lost downlink accelerates, and extrapolating today's average into the crewed-exploration era, when load is projected to rise substantially [\[17\]](#ref-17), [\[31\]](#ref-31), would understate the future penalty, possibly severely. This is why the load-response curve, not the satisfaction rate, is the externally valid object the dissertation foregrounds. The convexity reading has an established empirical precedent in another domain of fixed deadlines and tight coupling: megaproject costs follow a power-law driven by strong convexity, with fixed deadlines and tight coupling named among the generative drivers [\[61\]](#ref-61). The DSN shares those two drivers exactly: the viewing window is a fixed deadline and the missions are tightly coupled through the shared aperture, which is the cross-domain basis for expecting convexity rather than linearity. The interpretation to carry into the discussion chapter is that detecting convexity would not merely confirm H1 statistically; it would change the *object a planner is entitled to plan against*, from a point estimate of average loss to a curve that prices the system's accelerating fragility as load grows. That shift, from average to curve, is the practical payoff of taking the fat-tail question seriously, and it is why the dissertation refuses to let the satisfaction rate stand in for the distribution.


## 2.5 Synthesis: the integrated conceptual model the empirical work will test

The three frameworks are not three competing explanations; they are three complementary layers of a single conceptual model. Their synthesis is what the empirical chapters will test.

Queueing theory supplies the *formal model*. It defines the arrival process, the servers, the wait \(W_i\), the deadline-driven loss \(L_i\), and the disciplines that connect them, and it establishes through theorem that near-full utilization under a negotiated priority discipline with hard deadlines, bursty arrivals, and skewed service does not produce light-tailed waits [\[46\]](#ref-46), [\[80\]](#ref-80), [\[43\]](#ref-43), [\[45\]](#ref-45). It tells the dissertation *what to measure*: the shape of the wait distribution and the shape of the loss process, against an exponential null.

Forrester's system dynamics supplies the *structural cause*. It explains, at the level of stocks, flows, and delayed feedback, why the loss should concentrate rather than spread: locally optimizing missions, hedging under delay, pile their requests onto the same shared windows, and the relieving feedback is too slow to act within the window [\[23\]](#ref-23), [\[24\]](#ref-24), [\[25\]](#ref-25), [\[62\]](#ref-62), [\[63\]](#ref-63). With the inflow-shape corollary [\[19\]](#ref-19), [\[20\]](#ref-20) it tells the dissertation *which covariates matter*: the timing distribution of requests relative to geometry windows, operationalized as concurrent-mission load and viewing-window overlap, not the average load.
Taleb's program supplies the *statistical discipline and the risk reading*. It inverts the burden of proof so the exponential becomes a null to reject rather than an assumption to keep [\[27\]](#ref-27), and it makes the convex load-response the central testable signature of fragility [\[28\]](#ref-28), [\[29\]](#ref-29), [\[61\]](#ref-61). It tells the dissertation *how to test* and *why the answer matters for planning*: in Extremistan the average is a dangerous summary, and the load-response curve, not the satisfaction rate, is the object a planner needs.

Stitched together, the model yields the dissertation's falsifiable claim and its built-in null. The claim is that the science-throughput penalty from DSN antenna contention is heavy-tailed and concentrated on a minority of orbital-geometry and mission-phase windows (H1). The null is that it is roughly uniform and light-tailed (H0). The model does not assert H1 is true; it asserts that the structure of the system places the burden of proof on H0, and it specifies the empirical tests (heavy-tail fitting against the exponential, top-decile concentration share, convex load-response) by which either hypothesis can be accepted or refuted. The line of argument the chapter has built can now be stated compactly. The problem is real: the DSN is structurally oversubscribed under a deadline-bound priority discipline [\[10\]](#ref-10), [\[16\]](#ref-16), [\[35\]](#ref-35). The problem is material: lost downlink is lost science and degraded navigation tracking, growing with mission count and data rate [\[17\]](#ref-17), [\[31\]](#ref-31). The design addresses the causal mechanism: a queueing-plus-survival-plus-heavy-tail method measures exactly the tail and concentration that the Forrester-plus-queueing mechanism predicts [\[7\]](#ref-7), [\[8\]](#ref-8), [\[9\]](#ref-9), [\[4\]](#ref-4), [\[21\]](#ref-21). It beats the alternative: a mean satisfaction rate cannot, even in principle, distinguish Mediocristan from Extremistan, and the optimization-only literature never characterizes the residual penalty [\[10\]](#ref-10), [\[11\]](#ref-11), [\[27\]](#ref-27). The residual risk is acceptable: the burden-of-proof inversion, the pre-registered goodness-of-fit step, and the live, reportable null bound the danger of a false positive [\[27\]](#ref-27). This chapter has supplied the theoretical content behind each of these five propositions; the chapters that follow carry them into evidence and design.

A final scoping note fixes the chapter's boundary. This dissertation is a statistical and operations-research analysis of the distributional shape of a scheduling penalty. It does not design, field, or specify any system, capability, or data or service exchange. The architecture-traceability chain that a capability-development artifact would carry is therefore deliberately out of scope, and no enterprise-architecture vocabulary is forced onto what is, in substance, a queueing study. The decision relevance of the work rests entirely on the causal mechanism of Section 2.3 and on the lever analysis developed in the discussion chapter, which map the strategic objective (recover the most science return per dollar of constrained aperture) to a planning decision (broad versus targeted intervention) without an intervening architecture layer. The conceptual model stands complete; the empirical chapters take it from here.


# Chapter 3: Literature Review

## 3.0 The chapter's answer, and the problem it addresses

The scholarship on the Deep Space Network (DSN) scheduling problem is, taken as a whole, strong on two things and silent on a third, and that silence is exactly where this dissertation sits. The literature is strong on **mechanism**: it formalizes the allocation of antenna time as a hard combinatorial optimization and produces ever-better schedulers using constraint satisfaction, mixed-integer linear programming, evolutionary computation, reinforcement learning, and quantum annealing [\[32\]](#ref-32), [\[33\]](#ref-33). It is strong on **aggregate loading**: a parallel and largely separate forecasting literature projects future demand on the network, quantifies the gap between projected demand and current supply, and warns that crewed exploration, robotic proliferation, and rising per-mission data volumes are converging into a structural shortfall [\[31\]](#ref-31), [\[34\]](#ref-34). What this literature does **not** do, anywhere the public record can be searched, is characterize the statistical *shape* of the penalty that scheduling friction imposes after optimization has done its best. It reports the residual as a mean, typically a request-satisfaction rate or an oversubscription ratio, and a mean is precisely the summary statistic that cannot distinguish the two cases this dissertation tests: a penalty spread thinly and uniformly across all requests against a penalty concentrated heavily onto a minority of orbital-geometry and mission-phase windows.

The chapter reaches its answer by examining each body of work in turn. For each strand it states what the work found, the method by which it found it, the limitation that bounds the finding, and the way the finding relates to the gap. The reader arrives at the gap by elimination rather than by assertion: the optimization literature is reviewed first and shown to take demand as given and to report schedule quality, not penalty distribution (Section 3.1); the capacity and traffic-forecasting literature is reviewed next and shown to report aggregate loading, not a distribution over requests (Section 3.2); the broader ground-station and constellation contact-scheduling literature is reviewed third and shown to share the same optimization-and-aggregate posture even as it expands the methodological toolkit (Section 3.3); the methodological literatures this dissertation borrows, survival analysis, heavy-tail estimation, and concentration measurement, are reviewed for what they offer and have never yet been applied to (Section 3.4); and the gap is then stated explicitly, with the propositions that follow from it (Section 3.5).

The problem frame is as follows. The **current state** of the literature produces good schedules and good demand forecasts, and reports the residual penalty as an average. The **desired state** is a defensible, data-grounded characterization of the distributional shape of that penalty, its tail behavior and its concentration, grounded in the realized scheduling logs rather than in a summary mean. The **gap** is that no published treatment asks the distributional question; the optimization literature optimizes the schedule and the forecasting literature projects the load, and between them the realized request-to-allocation wait-time distribution and the realized lost-downlink distribution are never fit, tested, or decomposed. The **consequence** of leaving the gap unfilled is that capacity, scheduling-policy, and demand-negotiation investments are targeted on a mean that conceals which of two opposite remedial regimes applies, so that broad spending is applied where targeted spending would recover more science return, or the reverse, and exploration-era planning extrapolates from a misleading average rather than from a load-response curve. The confidence posture of this chapter is calibrated to that design-stage reality: the claim that the gap exists is a **high-confidence** claim, resting on an exhaustive and reproducible search of the published corpus and on the explicit reporting conventions of that corpus; the claim that the gap, once filled, will reveal concentration rather than uniformity is a **design-stage** claim about a mechanism, not an executed empirical finding, and is treated as such throughout.


## 3.1 DSN scheduling as optimization: strong on mechanism, silent on the residual distribution

### 3.1.1 The deployed scheduling environment and its reporting conventions

The canonical description of the operational DSN scheduling environment is given by Johnston and colleagues, whose account of the deployed scheduling engine and the integrated planning workflow is the reference point for nearly all subsequent work [\[10\]](#ref-10). Their contribution is a system description rather than an algorithm paper: it documents a multi-stage process that moves from long-range forecasting, through mid-range negotiation among missions, into near-real-time conflict resolution and execution, and it reports the deployment of a constraint-based scheduling tool, S4 and its successors, into routine operations. The method is software-engineering-and-operations-research applied at production scale, and the reported outcome is operational viability: schedules are produced, conflicts are reduced, and human schedulers are assisted rather than replaced. The companion mid- and long-range automation work extends the same workflow further up the planning horizon, automating the forecasting and negotiation stages that precede the near-real-time conflict resolution [\[13\]](#ref-13), and the integrated planning-to-real-time account by Hackett and colleagues closes the loop by describing how forecasting, mid-range, and real-time stages are stitched into one pipeline [\[16\]](#ref-16).

The **limitation**, for the purpose of this dissertation, lies in the reporting conventions these works establish, not in their substance, which is authoritative. The metrics they report are schedule-quality metrics: the number of conflicts resolved, the fraction of requests satisfied, the degree of automation achieved. Each of these is, by construction, an aggregate or a mean. The fraction of requests satisfied is the complement of the fraction lost, and it is a single number summarizing the whole network over a planning period. It says nothing about whether the unsatisfied fraction is scattered thinly across all missions and epochs or bunched onto particular geometry and phase windows. This is not a flaw in the work; it is the natural reporting unit for an operations team whose job is to produce a workable schedule. But it means that the published record, even at its most authoritative, carries the residual penalty only as a mean. The **relation to the gap** is direct: these works establish that the DSN is oversubscribed and that the schedule must drop or reduce some requests (the workflow that produces the request, allocation, and execution records this dissertation proposes to analyze is exactly the workflow these papers document), and they thereby establish the reality and the materiality of the problem, but they do not and were never intended to characterize the distribution of the loss.

### 3.1.2 The optimization formulations: MILP, evolutionary, reinforcement learning, quantum annealing

A succession of works reformulates the DSN allocation as a formal optimization problem and pursues better solvers. The framing of the allocation as multi-objective optimization under uncertainty, with evolutionary computation applied to it, is the early instance [\[12\]](#ref-12), [\[14\]](#ref-14). The mixed-integer linear programming (MILP) line is the most developed. Sabol and colleagues formulate the DSN scheduling problem as a MILP, state explicitly that the problem is **oversubscribed** so that only a subset of activities can be scheduled and operators must decide which to exclude, and develop a sequential algorithm that produces valid schedules for large instances using real DSN data from week 44 of 2016 [\[33\]](#ref-33). The Delta-MILP formulation by Claudet and colleagues advances this by targeting incremental schedule *changes* rather than full re-solves, which is the operationally relevant case because schedules are perturbed continuously rather than rebuilt from scratch [\[11\]](#ref-11). The reinforcement-learning formulation by Goh and colleagues casts the allocation as a sequential decision problem and learns a scheduling policy [\[15\]](#ref-15), and the quantum-annealing formulation by Guillaume and colleagues expresses the allocation as a quadratic unconstrained binary optimization (QUBO) problem and generates a schedule for one week of user antenna requests using a hybrid quantum-classical framework, while also documenting the network structure (three complexes, one 70-meter and several 34-meter antennas each, a few dozen missions served routinely) that bounds the supply side of the problem [\[32\]](#ref-32).

The convergent finding across this literature, interpreted for the argument, is that the DSN allocation is computationally hard, is genuinely oversubscribed in the sense that feasible schedules must exclude some requested activities, and admits no exact polynomial-time solution at operational scale, which is why the field keeps reaching for new solver paradigms. This convergence is itself evidence for the dissertation's premise: a problem that is provably oversubscribed and combinatorially hard does not have a costless optimal schedule; some requests are always lost, and the question of *which* requests, and whether the losses cluster, is left open by every one of these formulations. The method in each case is to fix the demand (the request set is an input) and optimize the assignment of fixed supply. The limitation is that these works optimize the schedule and report its quality; they do not characterize the statistical penalty that remains after optimization, and they cannot, because the objective function and the reported metrics describe the schedule produced, not the distribution of what the schedule had to drop. This limitation connects to the gap because optimizing a schedule and characterizing the distribution of its residual losses are different tasks requiring different methods: the former is combinatorial optimization, the latter distributional statistics. A field can be world-class at the first and silent on the second, and the DSN scheduling field is exactly that. The reporting record bears this out: across [\[32\]](#ref-32), [\[33\]](#ref-33), the reader will find satisfaction rates, conflict counts, and runtime comparisons, and will not find a fitted wait-time distribution, a tail-index estimate, or a concentration coefficient. One objection deserves an answer, namely that the optimization works implicitly contain the loss data, since they run on real request logs; this is true and is precisely the point: the data exist and the methods to analyze their distribution exist, but the two have not been joined, which is the opportunity this dissertation takes.

### 3.1.3 The demand-access alternative: an architectural response that still does not measure the penalty

A distinct strand proposes to change the *architecture* of access rather than only the schedule. Net and colleagues describe a DSN queuing antenna for demand access, motivated explicitly by the prospect that the advent of deep-space small spacecraft (MarCO, Lunar Trailblazer, Janus, EscaPADE, the thirteen Artemis-1 secondary payloads) will multiply the supported mission population over the coming decade and overwhelm the current scheduling approach [\[35\]](#ref-35). Their proposed integrated approach combines a queuing antenna that monitors many spacecraft and lets them transmit telemetry requests, a flexible near-real-time scheduling system that extends current DSN scheduling services, and a cloud-based ground data system that can scale on demand. This work is the closest in the corpus to naming the queue explicitly, and its motivation, a coming surge in the request population, is the same demand-side pressure this dissertation analyzes.

The interpretation for the argument is twofold. First, the demand-access proposal corroborates the dissertation's framing that the DSN is usefully read as a queue with requests that wait and are sometimes not served; the term "queuing antenna" is the operational community's own language for the problem. Second, the proposal is an engineering response to anticipated congestion, not a measurement of the congestion penalty's distribution. It designs a mechanism to absorb more requests; it does not fit the distribution of waits or losses under the current mechanism, and it does not test whether those losses are concentrated. Its relation to the gap is that it strengthens the first leg of the dissertation's argument, that the problem is real and growing (the same growth drivers appear in the forecasting literature reviewed next), while leaving the third leg, that a distributional method directly measures the predicted tail and concentration, entirely to be supplied. A queuing antenna and a queuing *analysis* are different artifacts; the literature has begun to build the former and has not begun the latter.

### 3.1.4 The supply side: fixed, lumpy aperture and the arraying alternative

The optimization and demand-access literatures take the supply of antenna time as a given input. A separate historical and engineering literature documents what that supply actually is, and reviewing it briefly matters for the dissertation because the *granularity* of the supply, large, discrete, expensively expanded apertures, is part of why the penalty might concentrate rather than smear. The DSN supply is not a continuously divisible resource; it is a small set of large dishes whose construction and upgrade are decade-scale capital events. The historical record of the large antennas, the first large Cassegrain antenna (Deep Space Station 11, Pioneer) and the first 34-meter high-efficiency antenna (Deep Space Station 15, Uranus), documents that each aperture is a discrete, individually engineered asset, and the 64-to-70-meter extension at Tidbinbilla documents that even enlarging an existing dish is a major undertaking rather than an incremental capacity adjustment [\[73\]](#ref-73), [\[72\]](#ref-72), [\[74\]](#ref-74). The arraying literature describes the principal way to extend effective aperture without building a new large dish: combining the signals of several smaller antennas to synthesize a larger effective collecting area, an approach whose background and rationale are documented in the arraying-techniques literature [\[71\]](#ref-71).

The **interpretation** for the dissertation is that the supply side is *lumpy*: capacity arrives in large, indivisible increments on long timescales, which means that when demand outpaces supply the system cannot respond by adding a marginal sliver of antenna time exactly where the contention is. This lumpiness interacts with the concentration hypothesis in a specific way. If the penalty were uniform, lumpy supply would still be a constraint but a simple one: add a dish, relieve everyone a little. If the penalty is concentrated on particular windows, lumpy supply is a sharper problem, because a new general-purpose dish relieves the carrying windows only to the extent those windows coincide with the new dish's geometry and band coverage, and arraying, which can be pointed and combined flexibly, may be the more targeted supply lever [\[71\]](#ref-71). The **limitation** of this supply literature, for the dissertation's question, is that it is descriptive and engineering-historical; it documents what the apertures are and how they can be combined, and it does not analyze how the fixed, lumpy supply maps onto the distribution of unmet demand. The **relation to the gap** is that it establishes the fixed-and-lumpy character of supply that, combined with growing and heterogeneous demand, sets up the contention whose distribution the dissertation measures, and it foreshadows the Chapter 7 lever analysis, in which arraying appears as a candidate *targeted* supply response if and only if the penalty proves concentrated.


## 3.2 DSN capacity and traffic forecasting: strong on aggregate loading, silent on the distribution over requests

### 3.2.1 The exploration-era demand projection

The forecasting literature establishes that demand on the DSN is growing and that the growth is structurally certain rather than speculative. Abraham and colleagues model DSN traffic for the human-exploration era and project the loading that crewed missions will add, distinguishing the short-but-tracking-intensive human lunar phase from the rising cadence of robotic and then crewed Mars activity [\[17\]](#ref-17). The expanded thirty-year-horizon analysis by Abraham and colleagues identifies three drivers of how the DSN must evolve: unparalleled growth in the number of robotic spacecraft, the emergence of tracking-intensive human exploration missions, and dramatic increases in per-mission data rate and data volume [\[31\]](#ref-31). This work is performed in support of the SCaN Program Systems Engineering Office and is presented to SCaN for strategic planning, which establishes both its authority and its reporting register: it is a capacity-planning input expressed in aggregate loading terms (network loading, spectrum, capability trends), projected forward.
The method is demand modeling: take the projected mission set and their stated data-return requirements, propagate them against the antenna supply, and report the resulting loading and the gap. The finding, interpreted for the argument, is that oversubscription is not a transient artifact of a particular year's mission mix but a structural and worsening feature driven by exogenous and certain trends. This finding is essential evidence for the dissertation's second proposition, that the problem is material and growing: lost downlink is lost science and degraded navigation tracking, and the volume at risk rises with mission count and data rate [\[31\]](#ref-31). The limitation is that the forecasting unit is aggregate loading, a network-wide or complex-wide projected demand, not a distribution over individual requests. A projected loading curve answers "how much total demand" and "how large the gap"; it does not answer "is the realized loss uniform or concentrated." The two questions are orthogonal: a network could be 130 percent loaded on average with the overload spread evenly across all requests, or 130 percent loaded with the overload bunched onto a few high-contention windows, and the loading forecast is identical in both cases while the remedial implication is opposite. The relation to the gap is therefore that the forecasting literature supplies the load context and the demand projections against which this dissertation's log-derived load covariates can be calibrated, and it motivates the analysis by establishing that the penalty is growing, but it does not and structurally cannot answer the distributional question.

### 3.2.2 The network-expansion and science-competition analyses

Two further works sharpen the aggregate picture. Malphrus and colleagues quantify the gap between projected demand and current supply for a specific science portfolio, the heliophysics system observatory, providing a worked instance of the demand-minus-supply shortfall that the general forecasts assert [\[18\]](#ref-18). The next-decade radio-science assessment documents how DSN time competes across mission classes, including the tension between spacecraft tracking and ground-based planetary radar and radio astronomy that share the same large apertures [\[34\]](#ref-34). The radio-astronomy survey by Lazio and Lichten makes the shared-aperture point concrete: the same 70-meter antennas at Canberra and Madrid that track spacecraft also conduct very-long-baseline interferometry and radio-astronomical observation, so science observing competes directly with operational tracking for the network's most capable assets [\[34\]](#ref-34).

The **interpretation** is that these works extend the materiality case to a second dimension: not only is total demand growing, but the demand is heterogeneous in kind (operational tracking, navigation, radar, radio astronomy), and these kinds compete for the same scarce apertures, which is exactly the structural condition under which a priority discipline must defer some subclass of requests. This heterogeneity-plus-shared-aperture structure is a **mechanism precondition** for the concentration this dissertation predicts: when different mission classes with different priorities and different deadline rigidities contend for the same antenna, the discipline that resolves the contention will systematically defer the lower-priority or more-flexible class, and systematic deferral of a subclass is one of the classical routes to a heavy wait-time tail. The **limitation** repeats the pattern: these works report which mission classes compete and how large the shortfall is, in aggregate, and do not fit a distribution of the resulting losses or test whether the losses concentrate on particular windows. The **relation to the gap** is that they establish the heterogeneity and shared-aperture preconditions that make concentration plausible, while leaving the test of concentration unperformed.

### 3.2.3 Why "aggregate loading" cannot answer the distributional question

The logical point deserves explicit statement, because it is the hinge between Sections 3.1, 3.2, and the gap. Both the optimization literature and the forecasting literature report the penalty through a mean: a satisfaction rate (optimization) or a loading ratio and demand-minus-supply gap (forecasting). A mean is a first moment. The distributional question this dissertation poses, is the loss light-tailed or heavy-tailed, and is it uniform or concentrated, is a question about the *shape* of the distribution: its tail index, its concentration coefficient, the share of loss carried by its worst decile. These are properties that a mean by construction discards. Two distributions with identical means can have entirely different tails and entirely different concentration. No amount of refinement of the mean, no better satisfaction rate and no more precise loading forecast, can ever answer the distributional question; the question requires distributional estimators applied to the realized losses. This is not a criticism of either literature, both of which report exactly what their tasks require, but it is the reason the gap is a true gap and not merely an under-explored corner: the existing reporting conventions are categorically incapable of producing the object the dissertation seeks, so the object must be produced by a different method. The **confidence** in this logical claim is high; it is a statement about what a first moment can and cannot encode, not an empirical claim about the DSN.


## 3.3 Ground-station and constellation contact-scheduling beyond the DSN: the same posture at larger scale

The DSN is one instance of a general class: the scheduling of contacts between orbiting assets and a constrained set of ground apertures. A substantial and methodologically rich literature addresses this general problem for Earth-observation constellations and low-Earth-orbit (LEO) mega-constellations, and reviewing it serves two purposes for this dissertation. First, it shows that the optimization-and-aggregate posture identified in Sections 3.1 and 3.2 is not a quirk of the DSN community but a field-wide convention. Second, it supplies the methodological vocabulary, pass shortening, cancellation, and movement under visibility-window constraints, that maps directly onto the DSN's pass-loss and reduction operations and onto this dissertation's variable constructs.

### 3.3.1 Mixed-integer and exact formulations

The Earth-imaging constellation scheduling work of Augenstein and colleagues formulates the joint scheduling of imagery collects, data downlinks, and health-and-safety contacts as a MILP, optimizing for maximal data throughput while respecting hardware-driven constraints (limited satellite agility) and operations-driven constraints (a minimum contact frequency per satellite), and it partitions the problem into sequential downlink and imaging steps with a dynamic-programming heuristic to run fast enough for human-operator interaction [\[37\]](#ref-37). The antenna-satellite scheduling work of Linares and colleagues is methodologically the most directly relevant to the dissertation's variable construction: their MILP "shaving model" allows the optimal planner to **cancel a pass, move it to another antenna, or shorten its duration** to avoid scheduling conflicts, after computing the passes generated by each satellite's windows of visibility [\[38\]](#ref-38). This is exactly the trichotomy, drop, reassign, or reduce, that the dissertation's pass-loss indicator and lost-downlink magnitude operationalize, and it confirms that "loss" in contact scheduling is not a single event but a graded one (full cancellation versus partial shortening), which is why the dissertation defines loss against a science-usefulness threshold rather than as a binary all-or-nothing.

The **interpretation** is that the general contact-scheduling literature has already named the operations, cancel, move, shorten, that produce lost downlink, and has built optimizers to minimize their cost. The **limitation**, again, is that the reported outcome is the optimized objective (throughput maximized, conflicts avoided), not the distribution of the cancellations, moves, and shortenings the optimizer was forced into. The **relation to the gap** is that this literature furnishes the dissertation's measurement vocabulary while exemplifying the same silence on distribution.

### 3.3.2 Multi-objective, evolutionary, and metaheuristic approaches

The multi-objective ground-station scheduling work of Petelin and colleagues solves the problem with six evolutionary multi-objective algorithms (NSGA-II, NSGA-III, SPEA2, GDE3, IBEA, MOEA/D) and reports their relative performance on benchmark instances of varying size, finding the Pareto-optimal trade-off front rather than a single weighted-sum solution [\[40\]](#ref-40). The genetic-algorithm work of Yang and colleagues addresses multi-ground-station and multi-satellite resource scheduling with an improved genetic algorithm [\[94\]](#ref-94), and the practitioner thesis of Wildish applies and tunes several commonly used heuristic algorithms to a real-world ground-station scheduling instance, documenting the practical constraints that arise when the operator must choose a subset of available access windows to best use the hardware [\[93\]](#ref-93). The capacity-orchestration model of de Carvalho optimizes the communication capacity of a ground-station network by coordinating handoffs as a satellite exits one station's field of view and another assumes tracking, extending total contact time to compensate for short LEO passes [\[42\]](#ref-42).

The convergent finding, interpreted for the argument, is that the field's standard move when contacts are oversubscribed is to deploy a better optimizer, exact, evolutionary, or metaheuristic, and to report the resulting schedule quality or Pareto front. Across these works the reported object is the optimized schedule and its quality metrics; none fits the distribution of the unscheduled or shortened passes, and none tests whether those losses concentrate. The limitation is therefore identical to the DSN case, now confirmed across an independent and larger literature, which makes it clear that the silence is field-wide and structural rather than incidental to one community. The uniform reporting pattern across [\[37\]](#ref-37), [\[38\]](#ref-38), [\[40\]](#ref-40), [\[94\]](#ref-94), [\[93\]](#ref-93), [\[42\]](#ref-42) confirms it: optimization objectives and quality metrics throughout, distributional characterization of residual loss nowhere.

### 3.3.3 Learning-based and distributed-architecture approaches, and a partial exception

The policy-gradient reinforcement-learning work of Dobariya and Hobiger schedules satellite-tracking tasks for LEO mega-constellations (OneWeb at roughly 650 satellites, Starlink at roughly 3500) using a transformer-based pointer network, and reports a reduction in the **mean number of missed satellites** of up to 54.3 percent versus a tuned greedy search and up to 29.5 percent versus dynamic programming, at the cost of modestly higher idle time [\[39\]](#ref-39). This is instructive precisely because the reported metric is the *mean* number of missed satellites: even the most modern learning-based scheduler in the corpus summarizes its loss as a mean, which is the reporting convention the dissertation argues is inadequate to the distributional question. The L2D2 distributed-ground-station design of Vasisht and colleagues takes the architectural route, using many low-cost geographically distributed stations with new scheduling and rate-adaptation algorithms to cut data-download latency from 90 minutes to 21 minutes, and it reports latency, a tail-relevant quantity, but as a headline reduction rather than as a fitted latency distribution with a characterized tail [\[92\]](#ref-92). The battery-aware contact-plan-design work of Fraire and colleagues is a partial methodological exception worth flagging: it models the on-board battery with both nonlinearities and **stochastic fluctuations in charge** so as to **control the risk of battery depletion**, which is a tail-risk-aware formulation in spirit, but the tail it manages is the battery-state tail, not the wait-time or pass-loss tail, and the management is via a contact-plan constraint rather than via distributional characterization of losses [\[41\]](#ref-41).

The **interpretation** is that the field is methodologically diverse and increasingly sophisticated, spanning exact MILP, evolutionary multi-objective optimization, deep reinforcement learning, distributed architecture, and even stochastic risk control, and yet across all of this diversity the residual loss is reported as a mean (missed-satellite count, satisfaction rate) or as a headline latency, never as a fitted distribution whose tail and concentration are estimated. The L2D2 latency result and the Fraire risk-control formulation are the closest the field comes to tail-awareness, and their distance from a distributional characterization of scheduling loss measures the size of the gap. The **relation to the gap** is that the dissertation's distributional treatment is novel not only for the DSN but for contact scheduling generally; no work in this independently assembled, methodologically broad literature fits the wait-time or pass-loss distribution, estimates its tail index, or measures its concentration.


## 3.4 The methodological literatures the dissertation imports, and where they have not yet been applied

The gap is not only that the question is unasked; it is that the methods to answer it, though mature in other fields, have never been brought to bear on contact-scheduling loss. This section reviews those methods as literature, establishing both their soundness and the fact that their application here is novel. The review covers three method families, queueing-theoretic tail results, survival analysis, and heavy-tail estimation and concentration measurement, and in each case states what the method establishes, by what evidence, and why its absence from the scheduling literature is the opportunity.

### 3.4.1 Queueing theory: tails are the rule, not the exception, under the DSN's structural conditions

The queueing literature is the formal bridge between "the schedule must drop some requests" and "the drops may be heavy-tailed and concentrated." Kendall's notation and embedded-Markov-chain analysis supply the vocabulary for describing the DSN as an arrival-server-wait system [\[8\]](#ref-8), and Kleinrock's treatment supplies the standard waiting-time results and the central caution that queueing systems do not generally produce light-tailed waits [\[7\]](#ref-7). The Terekhov and colleagues synthesis of queueing theory with scheduling is the most directly relevant: it studies dynamic scheduling problems in which the choice of queue discipline shapes the realized wait distribution, which is exactly the DSN's situation, where a negotiated priority-and-preference discipline allocates antenna time and thereby determines which subclass of requests waits longest [\[9\]](#ref-9).

A substantial body of results establishes that the DSN's specific structural features are known generators of heavy tails. First, **deadline-driven abandonment**: the DSN viewing geometry imposes a hard window close, so a request not served before its window passes is lost rather than merely delayed, which is the impatient-customer or reneging structure. The multiserver-with-impatient-customers analysis of Boots and Tijms gives the loss probability for exactly this structure [\[48\]](#ref-48); the processor-sharing-with-impatience fluid limits of Gromoll and colleagues and the reneging processor-sharing analysis show that impatience substantially changes the queue's behavior relative to the patient case [\[49\]](#ref-49), [\[95\]](#ref-95); the diffusion approximations for networks with reneging extend this to networked settings [\[84\]](#ref-84); and the deadline-reward scheduling analysis of Raviv and Leshem treats the case where each request carries a deadline and a reward, which maps onto the DSN's mission-criticality weighting [\[50\]](#ref-50). Second, **bursty and self-similar arrivals**: the Leland and colleagues demonstration that Ethernet traffic is statistically self-similar with no natural burst length, so that aggregating streams intensifies rather than smooths burstiness, is the foundational result that bursty arrivals are a route to heavy tails [\[51\]](#ref-51), extended by the delay-bound analysis of Liebeherr and colleagues for heavy-tailed and self-similar traffic [\[52\]](#ref-52). The DSN's arrivals are bursty by construction because requests cluster on the geometry windows when many targets are simultaneously well placed. Third, **priority disciplines that freeze out a subclass**: the Barabasi-style queueing results of Vazquez and colleagues and Blanchard and Hongler show that priority-based scheduling alone generates heavy-tailed waiting times, because low-priority tasks stay unserved while high-priority tasks are served rapidly [\[83\]](#ref-83), [\[82\]](#ref-82). The DSN schedule is a priority-and-preference discipline, the precise structure these results address.

Complementing these, the heavy-traffic and multiserver tail literature characterizes when waits remain light-tailed and when they do not, and it rewards careful reading because the DSN is, structurally, a small-server-count multiclass system rather than the large-server-pool systems for which the most reassuring (asymptotically exponential) tail results hold. The Halfin-Whitt-regime analysis of Gamarnik and Stolyar derives bounds on the steady-state queue length for a heterogeneous multiclass many-server system, but explicitly in the regime where the number of servers grows large and the utilization approaches one as one minus a constant over the square root of the server count [\[43\]](#ref-43); the DSN, with one 70-meter and a handful of 34-meter antennas per complex [\[32\]](#ref-32), sits far from that large-pool limit, so the favorable concentration-of-waits results of the many-server regime do not automatically transfer. The multiclass many-server scheduling analysis of Atar and colleagues similarly establishes asymptotic optimality in a regime where the server count and offered load scale together [\[45\]](#ref-45), again a large-pool result. Against these, the Markov-modulated M/G/1 waiting-time-tail result of Asmussen and O'Cinneide shows that modulation of the arrival environment, exactly the geometry-clustering that modulates the DSN arrival rate, governs the decay rate of the waiting-time tail [\[80\]](#ref-80); the asymptotic-exponentiality result for the Ph/Ph/c waiting time of Takahashi characterizes precisely when a multiserver wait tail is exponential and identifies the parameter that controls the decay [\[46\]](#ref-46); and the SRPT and EDF heavy-traffic diffusion limits of Kruk explicitly admit heavy-tailed inter-arrival and service distributions and carry them into the limiting wait behavior [\[85\]](#ref-85). Together these establish that the tail behavior of a multiserver queue depends sharply on the arrival and service distributions and on the discipline, that heavy service-time tails or heavy arrival bursts propagate into heavy waiting-time tails, and that the favorable light-tail results require a large server pool the DSN does not have. The Coffman-Kleinrock feedback-queue analysis grounds the priority-discipline case historically, showing how a feedback discipline that defers customers by required-service length shapes the conditional wait [\[44\]](#ref-44), and the DHR-tail scheduling result of Aalto and Ayesta connects service-time tail shape to optimal discipline, establishing that when the service tail has decreasing hazard rate the optimal policy gives priority to the youngest jobs, which systematically and indefinitely defers the oldest, a mechanism that directly produces a heavy wait tail for the deferred subclass [\[81\]](#ref-81).

Interpreted for the argument, this literature carries a clear conclusion: under the DSN's structural conditions, the burden of proof should sit on the light-tailed null, not on the heavy-tailed alternative. The DSN simultaneously exhibits all three classical heavy-tail generators, deadline-driven abandonment [\[48\]](#ref-48), [\[49\]](#ref-49), [\[95\]](#ref-95), [\[84\]](#ref-84), [\[50\]](#ref-50), bursty and self-similar arrivals [\[51\]](#ref-51), [\[52\]](#ref-52), and a priority discipline that defers a subclass [\[83\]](#ref-83), [\[82\]](#ref-82), and each of these mechanisms is independently and theoretically established to produce heavy waiting-time tails even at moderate average load [\[43\]](#ref-43), [\[46\]](#ref-46), [\[85\]](#ref-85). The cited results are mathematical theorems and validated empirical demonstrations, not analogies, drawn from queueing theory and network traffic analysis. The conclusion must be read with care: the queueing literature establishes the *mechanisms* by which the DSN tail *could* be heavy; it does not establish that the DSN tail *is* heavy, because no queueing result has been fit to DSN logs, which is the empirical step the dissertation reserves. The reasonable objection is that these results are drawn from general operations-research and telecommunications settings, not from space operations, so the mapping to the DSN is a transfer-of-mechanism argument made by construction (the viewing-window-as-deadline, the geometry-clustering-as-burst, the mission-priority-as-discipline mappings of Chapter 2) rather than a prior space-domain empirical result; this transfer is the dissertation's explicit and examiner-flagged assumption, and the empirical test is built precisely to confirm or refute it. The relation to the gap is that the queueing literature predicts the heavy tail that the scheduling literature never measures, and the dissertation joins them.
### 3.4.2 Survival analysis: the right tool for censored time-to-allocation, never applied to scheduling logs

The dissertation models the time from request submission to allocation as time-to-event data with right-censoring, because some requests are still pending at the observation cutoff and some expire when their window closes without ever being allocated. The survival-analysis literature supplies the estimators. The Kaplan-Meier nonparametric survival estimator handles the censoring without parametric assumptions [\[2\]](#ref-2), and the Cox proportional-hazards model gives the covariate-adjusted hazard of the event (here, allocation) as a function of geometry, band, and load [\[1\]](#ref-1), with the Therneau-Grambsch treatment extending the Cox model to time-varying covariates, which matters because concurrent load changes while a request waits [\[3\]](#ref-3). The competing-risks framework of Andersen and colleagues applies directly: a waiting DSN request faces two competing terminal events, allocation and expiry, and the naive Kaplan-Meier that treats the competing event as censored is biased. Competing-risks methods are required to separate the cause-specific hazard of allocation from the cause-specific hazard of expiry [\[64\]](#ref-64). The pedagogical treatments of Schober and Vetter and of Andrade establish that survival times are typically skewed, which limits methods assuming normality and motivates the time-to-event approach [\[65\]](#ref-65), [\[66\]](#ref-66), and the Mills text provides the event-history framework and the relation among the survivor, density, and hazard functions [\[89\]](#ref-89). The Guyot and colleagues reconstruction method, which recovers approximate individual time-to-event data from published Kaplan-Meier curves, is a contingency the dissertation flags for intervals where raw log access is constrained and only aggregated summaries are available [\[88\]](#ref-88).

The **interpretation** is that survival analysis is a mature, standard methodology with off-the-shelf estimators for exactly the censored-time-to-allocation structure the DSN request stream presents, and that the competing-risks refinement is not optional but necessary given the allocation-versus-expiry duality. The **limitation** of the existing survival literature, for this purpose, is only that it is developed and validated overwhelmingly in biomedical and epidemiological settings [\[64\]](#ref-64), [\[65\]](#ref-65), [\[66\]](#ref-66), so its application to antenna-allocation waits is a domain transfer; the transfer is methodologically safe because the censoring structure is identical (an event that may or may not occur by the observation cutoff), but it has not been done. The **relation to the gap** is that the scheduling literature reports satisfaction rates, which throw away the *timing* information entirely (a request satisfied late and a request satisfied immediately count the same in a satisfaction rate), whereas survival analysis preserves and models the timing, which is half of the distributional object the dissertation seeks. No work in the scheduling corpus applies survival analysis to allocation waits; this is a clean methodological novelty.

### 3.4.3 Heavy-tail estimation and concentration measurement: disciplined tools, never applied to scheduling loss

The dissertation's central empirical claims are distributional, and the methods to fit and test distributions are mature. The Clauset-Shalizi-Newman framework is the standard for fitting and testing power-law distributions in empirical data. It combines maximum-likelihood estimation of the tail with a goodness-of-fit step and a likelihood-ratio comparison against alternatives, and it disciplines heavy-tail claims against the well-known tendency to over-detect power laws [\[4\]](#ref-4). Its implementations, the powerlaw Python package of Alstott and colleagues and the poweRlaw R package of Gillespie, make the framework operational with bootstrap goodness-of-fit [\[5\]](#ref-5), [\[6\]](#ref-6). The extreme-value-theory line supplies the upper-tail estimator: McNeil's application of the generalized Pareto distribution (GPD) to loss-severity tails under the peaks-over-threshold framework is the foundational reference [\[54\]](#ref-54), extended by the peaks-over-threshold tail-risk estimation of Zhao and colleagues [\[58\]](#ref-58), the Bayesian threshold-estimation approach of Behrens and colleagues that treats the threshold as uncertain rather than fixed empirically [\[57\]](#ref-57), the multivariate-extremes conditional approach of Heffernan and Tawn and the multivariate GPD of Rootzen and Tajvidi for joint-tail behavior [\[55\]](#ref-55), [\[56\]](#ref-56), the gradient-boosting extreme-quantile-regression method of Velthoen and colleagues for covariate-dependent tails [\[96\]](#ref-96), and the phase-type scale-mixture fitting of Bladt and Rojas-Nandayapa for fitting both body and tail of heavy-tailed data simultaneously [\[59\]](#ref-59). The friendship-paradox sampling result of Nettasinghe and Krishnamurthy and the modified-Lomax model of Chattopadhyay and colleagues address the estimation difficulties that arise when tail data are scarce [\[86\]](#ref-86), [\[87\]](#ref-87), a relevant caution given that the rarest, worst windows are by definition undersampled.

For the concentration half of the distributional object, the inequality-measurement literature supplies the estimators. The Gini index, reviewed by Farris with two interpretive characterizations, measures how equitably a resource is distributed across a population [\[76\]](#ref-76), and is the natural summary for "how concentrated is lost downlink across windows." The Deltas analysis of the Gini coefficient's small-sample downward bias is a necessary caution because the geometry-phase windows may be few in some strata, so the Gini must be bias-corrected when window counts are small [\[77\]](#ref-77). The concentration-index estimation methods of O'Donnell and colleagues and the broader inequality-measures glossary of De Maio supply the curve-based and entropy-based alternatives (concentration curves, generalized-entropy and Atkinson indices) that let the dissertation report concentration with more nuance than a single Gini and probe different regions of the loss distribution [\[78\]](#ref-78), [\[79\]](#ref-79). The self-similar-traffic loss analysis of Zhuang and Li, which examines packet loss under heavy-tailed and self-similar arrivals, is the nearest the corpus comes to applying tail-aware loss analysis in a contact-relevant (network-traffic) setting, and even it analyzes packet loss under given arrival processes rather than the concentration of scheduling loss across structural windows [\[53\]](#ref-53).

Interpreted for the argument, this methodological literature establishes a second clear conclusion: the methods required to answer the distributional question exist, are mature, and are disciplined against their own failure modes. Heavy-tail fitting has a standard maximum-likelihood-plus-goodness-of-fit protocol [\[4\]](#ref-4), [\[5\]](#ref-5), [\[6\]](#ref-6) and a standard extreme-value upper-tail estimator [\[54\]](#ref-54), [\[58\]](#ref-58); concentration has standard estimators with known bias corrections [\[76\]](#ref-76), [\[77\]](#ref-77), [\[78\]](#ref-78). A question about distributional shape is answerable if and only if validated distributional estimators can be applied to the realized data, and they can, since each cited method is a published, peer-reviewed, and in most cases software-supported statistical procedure with established properties. Two cautions attach to the conclusion. First, these methods are imported from econometrics, epidemiology, network traffic analysis, and reliability; their soundness is established in those domains, and the dissertation's contribution is to apply them, not to invent them, so the methodological risk is low but the application is unprecedented in this domain. Second, no precedent applies Gini or top-decile concentration, or Clauset-Shalizi-Newman heavy-tail fitting, to ground-station or DSN scheduling loss specifically [\[76\]](#ref-76), [\[78\]](#ref-78), [\[53\]](#ref-53), which is simultaneously the novelty of the dissertation and a thinness the examiner should weigh: the method transfer is sound but is being made for the first time, so there is no domain-specific precedent to calibrate against, and the dissertation's pre-registered decision rules and goodness-of-fit gates are the safeguard against the transfer producing false positives. The relation to the gap is that these methods are the supply side of the answer; the question has been unasked not because it was unanswerable but because the answering methods sit in different fields from the scheduling community, and the dissertation's move is to cross that disciplinary boundary.

### 3.4.4 Why the distributional question is rarely asked: a structural-dynamics reading

A reasonable reader may ask why, if the data exist in one field and the methods in another, the join has not already been made. The system-dynamics and operations-management literature supplies a structural answer, and reviewing it both explains the gap's persistence and connects this chapter to the theoretical framework that precedes it. The core insight of that tradition, due to Forrester, is that the behavior of a contested system is dominated by its loop structure and delays rather than by the visible intentions of the actors, which produces counterintuitive *concentration* of effects that local, actor-level reasoning does not anticipate [\[21\]](#ref-21). When a field reasons about a scheduling system from the scheduler's seat, the natural questions are local and aggregate, how good is this schedule, what is the satisfaction rate, and the structural question, where does the unmet demand pile up and why, requires stepping back to the stock-flow-feedback view that system dynamics provides.

The supporting literature makes the mechanism concrete and shows it is not DSN-specific. The Sterman and colleagues survey of system-dynamics modeling opportunities in operations management documents that core operational processes involve feedbacks with delays, nonlinearities, and information distortions that generate complex dynamics invisible to static optimization [\[62\]](#ref-62), and the bathtub-dynamics result of Sweeney and Sterman demonstrates empirically that even educated subjects systematically fail to infer how a stock (a backlog) accumulates from its inflows and outflows, which is precisely the cognitive failure that leads a scheduling field to track flows (requests, allocations) while never characterizing the accumulated backlog stock's distribution [\[25\]](#ref-25). The order-stability-in-supply-chains experiments of Croson and colleagues show that coordination risk, individuals acting on locally rational rules without certainty about others' behavior, amplifies oscillation and concentration in a contested ordering system, the direct analogue of missions padding and escalating requests without certainty about competitors' behavior [\[63\]](#ref-63). The aerospace-and-defense systems-dynamics study of Bindra and colleagues applies stock-and-flow and causal-loop modeling to delays in component delivery, showing how feedback and delay exacerbate disruption and identifying intervention points, a worked instance of the same structural reading in an adjacent space-systems setting [\[90\]](#ref-90). Inflow-shape results from the orbital-environment literature reinforce the central point that the *temporal distribution* of an inflow, not merely its total, determines whether a stock stabilizes or runs away: the launch-rate-distribution dynamical analysis of D'Ambrosio and colleagues and the orbital-debris population-dynamics treatment of Lewis both show that the same total inflow produces stable or divergent stock behavior depending on its timing distribution [\[19\]](#ref-19), [\[20\]](#ref-20).

The interpretation is that the gap persists not because the question is uninteresting but because answering it requires a methodological and conceptual posture, distributional and structural, that is orthogonal to the optimization-and-aggregate posture native to the scheduling field. The limitation of the system-dynamics literature for the dissertation is that it is largely qualitative or simulation-based and does not itself supply the realized-data distributional estimators (those come from Section 3.4.3); its role is explanatory, telling us *why* concentration is structurally plausible and why the question has been overlooked, not *how* to measure the concentration. The relation to the gap is that this literature is the conceptual reason to expect the gap to be substantive rather than empty: if Forrester is right that loop structure and delay concentrate effects counterintuitively, then the realized DSN loss is more likely concentrated than uniform, and the field's failure to ask the distributional question is itself a predictable consequence of reasoning from the scheduler's local seat rather than from the system's structural view.


## 3.5 The gap, stated explicitly, and the propositions that follow

### 3.5.1 The gap

The literature reviewed in this chapter divides cleanly into three postures with respect to the dissertation's question, and the gap is the empty cell that the division reveals.

The first posture, the DSN and contact-scheduling **optimization** literature [\[32\]](#ref-32), [\[33\]](#ref-33), [\[37\]](#ref-37), [\[38\]](#ref-38), [\[40\]](#ref-40), [\[39\]](#ref-39), [\[94\]](#ref-94), [\[93\]](#ref-93), [\[42\]](#ref-42), [\[41\]](#ref-41), [\[92\]](#ref-92), [\[35\]](#ref-35), takes demand as given and produces better allocations of fixed supply, reporting schedule-quality metrics that are means: satisfaction rates, conflict counts, missed-satellite counts, latency headlines. This posture is strong on mechanism and silent on the residual distribution.

The second posture, the **capacity and traffic-forecasting** literature [\[31\]](#ref-31), [\[34\]](#ref-34), projects future demand and quantifies the aggregate shortfall, reporting loading ratios and demand-minus-supply gaps that are also aggregates. This posture is strong on aggregate loading and silent on the distribution over requests.

The third posture, the **methodological** literatures the dissertation imports, queueing-tail theory [\[48\]](#ref-48), [\[49\]](#ref-49), [\[95\]](#ref-95), [\[84\]](#ref-84), [\[50\]](#ref-50), [\[51\]](#ref-51), [\[52\]](#ref-52), [\[83\]](#ref-83), [\[82\]](#ref-82), [\[43\]](#ref-43), [\[45\]](#ref-45), [\[80\]](#ref-80), [\[46\]](#ref-46), [\[85\]](#ref-85), [\[44\]](#ref-44), [\[81\]](#ref-81), [\[47\]](#ref-47), survival analysis [\[64\]](#ref-64), [\[65\]](#ref-65), [\[66\]](#ref-66), [\[89\]](#ref-89), [\[88\]](#ref-88), heavy-tail and concentration estimation [\[54\]](#ref-54), [\[58\]](#ref-58), [\[57\]](#ref-57), [\[55\]](#ref-55), [\[56\]](#ref-56), [\[96\]](#ref-96), [\[59\]](#ref-59), [\[86\]](#ref-86), [\[87\]](#ref-87), [\[76\]](#ref-76), [\[77\]](#ref-77), [\[78\]](#ref-78), [\[79\]](#ref-79), [\[53\]](#ref-53), and the structural system-dynamics reading that explains the gap's persistence [\[25\]](#ref-25), [\[62\]](#ref-62), [\[63\]](#ref-63), [\[90\]](#ref-90), [\[19\]](#ref-19), [\[20\]](#ref-20), together predict that the DSN penalty *could* be heavy-tailed and concentrated, supply the estimators to test it, and explain why the question has been overlooked, but have never been applied to DSN or contact-scheduling loss.

The gap is the intersection of these three postures' silences: **no published treatment fits the realized request-to-allocation wait-time distribution or the realized lost-downlink distribution for the DSN (or for contact scheduling generally), tests its tail against a light-tailed null, or measures its concentration across structural windows.** The optimization literature has the data and the operational question but reports a mean; the forecasting literature has the demand context but reports an aggregate; the methodological literatures have the estimators but have never been pointed at this target. The mean and the aggregate are, as Section 3.2.3 argued on first principles, categorically incapable of answering the distributional question, so the gap cannot be closed by refining either; it requires the methodological import the dissertation supplies. The **confidence** in the existence of this gap is high, resting on an exhaustive, deduplicated, and reproducibly assembled corpus search across the optimization, forecasting, queueing, survival, and heavy-tail literatures, and on the explicit and uniform reporting conventions of the first two.

A scope honesty note belongs here. The dissertation's gap is, in part, *expected* to be empty of prior distributions: there is no published DSN-specific empirical wait-time or pass-loss distribution to benchmark against, because producing one is the contribution. The consequence is that the empirical chapters rely on the realized logs themselves rather than on a prior published distribution, and they cross-check derived load covariates against the aggregate loading reports [\[31\]](#ref-31) rather than against a prior distributional result. This is a genuine thinness of the corpus, stated plainly so the examiner can weigh it, and it is also the precise reason the contribution is a contribution rather than a replication.

### 3.5.2 Positioning the contribution in the gap

The contribution sits exactly in the empty cell. It joins the three postures: it takes the realized loss data that the optimization literature generates but reports only as a mean; it uses the aggregate loading context that the forecasting literature supplies to calibrate the load covariate; and it applies the queueing-predicted, survival-and-heavy-tail-estimated distributional methods that the third literature has developed but never applied here. The contribution is therefore neither a new scheduler (the optimization field is well served) nor a new demand forecast (the forecasting field is well served) but a new *characterization*: a falsifiable distributional claim about the shape of the penalty, tested with pre-registered rules. The dissertation's place in the literature is the bridge between a field that measures the schedule and a field that measures the load, supplying the missing measurement of the distribution of what the schedule, given the load, is forced to lose.

### 3.5.3 The propositions that follow from the gap

From the gap and the literature that frames it, three propositions follow, each stated with its grounding literature, its mechanism, and its design-stage confidence. These propositions are the literature-derived form of the H0/H1 contribution that the research design (Chapter 5) and analysis plan (Chapter 6) operationalize and test; they are not findings.

**Proposition 1 (tail).** The realized request-to-allocation wait-time distribution and the realized pass-loss distribution will exhibit heavy upper tails better described by a power-law, log-normal, or generalized-Pareto tail than by an exponential. The **mechanism** is the convergence of three independently tail-generating queueing structures present in the DSN by construction, deadline-driven abandonment under hard viewing-window closes, bursty geometry-clustered arrivals, and a priority discipline that systematically defers a subclass [\[48\]](#ref-48), [\[49\]](#ref-49), [\[95\]](#ref-95), [\[50\]](#ref-50), [\[51\]](#ref-51), [\[83\]](#ref-83), [\[82\]](#ref-82), [\[85\]](#ref-85), each of which is established to produce heavy waits at moderate load. The **confidence** is design-stage: the mechanism is theoretically well-supported, and whether the DSN logs actually show the heavy tail is the empirical question the design is built to answer. The **falsifier** is a wait-time tail statistically indistinguishable from exponential under the Clauset-Shalizi-Newman likelihood-ratio test and a non-positive generalized-Pareto shape parameter [\[54\]](#ref-54), [\[58\]](#ref-58).
**Proposition 2 (concentration).** Lost downlink will concentrate on a minority of geometry-phase windows, so that the share carried by the top decile of windows exceeds the ten percent that uniformity predicts and the Gini coefficient of loss across windows is correspondingly high. The **mechanism** is the shared-aperture, heterogeneous-mission-class contention documented in the forecasting and radio-science literature [\[34\]](#ref-34), [\[31\]](#ref-31), in which different mission classes with different priorities and deadline rigidities contend for the same scarce apertures, so that the discipline defers a consistent subclass onto consistent windows. Locally optimizing request behavior (early submission, duration padding, priority escalation) amplifies the effect, as the demand-access motivation literature anticipates [\[35\]](#ref-35). The **confidence** is design-stage. The **falsifier** is a top-decile loss share near ten percent and a low, small-sample-corrected Gini coefficient [\[76\]](#ref-76), [\[77\]](#ref-77), [\[78\]](#ref-78).

**Proposition 3 (conditional drivers and load-response).** Pass-loss probability will be elevated in conjunction-driven viewing-overlap windows, in the most contested band, and at the highest concurrent-load quartile, and the lost-downlink-versus-load relationship will be convex (accelerating) rather than linear. The **mechanism** is that contention rises faster than load when locally optimal requests pile onto shared windows whose relieving feedback operates with a delay longer than the window. That convexity is the fragility signature, and the conditional associations are estimable with the survival and regression methods imported in Section 3.4 [\[64\]](#ref-64), [\[47\]](#ref-47). The **confidence** is design-stage, and it is the lowest of the three. Convexity of the load-response curve is the clause whose mechanism, looped delayed feedback, the cross-sectional design tests only through the convex signature rather than establishes causally. That boundary is stated plainly here and carried into the design and discussion chapters. The **falsifier** is flat conditional associations and a linear or concave load-response curve.

The acceptance rule that binds these propositions, fixed verbatim from the dissertation's contribution, is that the central claim is accepted only if **both** the tail clause (Proposition 1) **and** the concentration clause (Proposition 2) pass their pre-registered tests. Either failing refutes the contribution, and that refutation is itself a reportable and decision-relevant result, because it would redirect remedial investment from targeted to broad. Proposition 3 sharpens and localizes the claim but is not part of the binding acceptance rule. This structure, two binding clauses with a live null and a clean refutation path, is what makes the contribution falsifiable rather than rhetorical, and it is the literature gap of Section 3.5.1 that makes the test worth running: the question has the data, has the methods, and has never been asked.

### 3.5.4 How this chapter advances the argument

Across its sections the chapter has advanced the five propositions on which the dissertation rests. The ledger now stands as follows. The problem is real: the optimization literature establishes that the DSN is genuinely oversubscribed and must drop requests [\[33\]](#ref-33), [\[32\]](#ref-32), [\[35\]](#ref-35), and the contact-scheduling literature confirms the same condition field-wide [\[38\]](#ref-38), [\[93\]](#ref-93). The problem is material and growing: the forecasting literature establishes that the lost-downlink volume rises with mission count, data rate, and shared-aperture science competition [\[31\]](#ref-31), [\[34\]](#ref-34). The intervention addresses the mechanism: the queueing, survival, and heavy-tail literatures supply methods that measure the tail and concentration the mechanism predicts [\[48\]](#ref-48), [\[54\]](#ref-54), [\[76\]](#ref-76). It beats the alternatives: the status-quo mean (satisfaction rate, loading ratio) cannot distinguish uniform from concentrated, as Section 3.2.3 proved on first principles, and the optimization-only literature does not characterize the residual at all [\[33\]](#ref-33), [\[39\]](#ref-39). The residual risk is acceptable: the heavy-tail and concentration methods carry their own disciplines against false positives, pre-registered goodness-of-fit, bias-corrected Gini, threshold-stability diagnostics, and the null is a live and reportable outcome [\[77\]](#ref-77), [\[57\]](#ref-57). The chapter's work is to ground each of these propositions in the reviewed literature and to hand the empirical test, clean and falsifiable, to the chapters that follow.


# Chapter 4: Data and Measurement

## 4.0 The chapter's answer

The distributional question at the center of this dissertation is answerable from data that already exist as a byproduct of running the Deep Space Network (DSN). Three named records, taken together, supply every construct the design needs, and each carries a known and bounded bias that the measurement strategy must absorb rather than ignore. The records are the DSN scheduling and tracking logs exposed through the service catalog and the Service Preparation Subsystem (SPS) schedule archives, the loading and traffic-forecasting reports hosted on the NASA Technical Reports Server (NTRS), and the per-mission downlink-requirement and critical-event records held in mission service agreements. From these, the chapter constructs the wait time of a request, the binary indicator that a requested pass was lost, the physical magnitude of the lost downlink, and the covariate vector of orbital geometry, frequency band, concurrent load, and mission phase that the hypotheses require. The central measurement claim, stated first so the sections that follow develop rather than withhold it, is that the request log is not a clean demand signal but a hedged one. Missions submit early and pad requested durations because the schedule may cut them, so requested time systematically overstates true need, and the entire measurement apparatus is built to treat the request as a strategic artifact rather than a transparent statement of need. What follows operationalizes the prospectus data section into a codebook, names the biases that threaten each construct, and specifies how each construct is validated against an independently reported value before any estimation is attempted.

A note on posture, carried from Chapter 1 and binding on every empirical sentence in this chapter. This is a design-stage dissertation. No DSN log has been retrieved or parsed; no wait-time has been computed; no concentration coefficient has been measured. The datasets named here are real artifacts of DSN operations and of the NASA reporting system, and the access paths described are the actual interfaces through which those artifacts are exposed, but the chapter describes a measurement plan that has not been executed. Where the chapter states what a variable would equal or how a distribution would be shaped, the conditional is load-bearing and deliberate. The confidence attached to the proposition that these records contain the needed constructs is high, because the operational literature documents the workflow that produces them [\[10\]](#ref-10), [\[16\]](#ref-16); the confidence attached to any statement about the realized values in those records is, by construction, undetermined until the design is run.

## 4.1 The problem this chapter addresses

### 4.1.1 Current state

The current state of measurement in the DSN-contention literature is that the penalty of oversubscription is reported, when it is reported at all, as an aggregate satisfaction rate or as a projected aggregate shortfall. The optimization literature evaluates a candidate schedule by the fraction of requested activities it manages to place, and it calibrates that evaluation on a slice of real demand, for example a single week of user antenna requests, treated as a benchmark instance rather than as a sample from a distribution to be characterized [\[33\]](#ref-33), [\[32\]](#ref-32). The traffic-forecasting literature models projected demand out to a multi-decade horizon and reports the loading trends that the network must absorb, again as aggregates by complex, band, and epoch [\[17\]](#ref-17), [\[31\]](#ref-31). Both bodies of work touch the same records this dissertation needs, but neither converts those records into the request-level and window-level measured quantities that a distributional analysis requires. The data are produced; the measured constructs are not.

### 4.1.2 Desired state

The desired state is a request-level panel in which every requested tracking activity carries a measured wait time with a censoring flag, a measured pass-loss indicator, a measured lost-downlink magnitude in physical units, and a measured covariate vector, together with a window-level aggregation of lost downlink onto the geometry-phase cells over which concentration is defined. That panel is the object on which Chapters 5 and 6 estimate the survival model, fit the heavy-tail distributions, and compute the concentration metrics. The desired state is not merely the possession of the raw logs; it is the disciplined transformation of each operational record into a construct with a defined scale, a stated source, a known bias, and a validation against an independent value. The gap between the produced data and the desired measured panel is exactly the work this chapter specifies.

### 4.1.3 Gap and consequence

The gap is a measurement gap, not a data-availability gap in the first instance, although access constraints (Section 4.7) reintroduce an availability problem for some intervals. The consequence of leaving the gap unfilled is that the distributional question cannot be asked: without a request-level wait time and a window-level loss aggregation, there is no distribution to fit and no concentration to measure, and the field is left with the mean it already has. Filling the gap carelessly is worse than not filling it, because a request log read naively as demand would import the missions' strategic padding directly into the dependent and independent variables and would manufacture apparent contention out of hedging behavior. The chapter therefore treats careful operationalization, with explicit bias handling, as the precondition for the entire empirical contribution. This is what it means for the intervention to address the mechanism: the measured constructs are defined so that they capture the tail and the concentration the mechanism predicts, rather than artifacts of how missions ask for time.

## 4.2 Named datasets in depth

The analysis draws on three named data sources. Each is described here in terms of provenance, the unit it natively records, its coverage, its access path, and its characteristic biases. The three are complementary: the scheduling and tracking logs supply the request-level events, the NTRS reports supply the validated aggregate context against which the log-derived measures are checked, and the mission records convert a lost pass into a quantified and, where possible, criticality-weighted science loss.

### 4.2.1 DSN scheduling and tracking logs

**Provenance.** The scheduling and tracking logs are the operational record of the DSN allocation process. The DSN allocates antenna time through a multi-stage workflow that moves from long-range forecasting, through mid-range negotiation among missions, to near-real-time conflict resolution and execution; this workflow is documented in the canonical descriptions of the deployed scheduling environment [\[10\]](#ref-10) and of the integrated planning-and-scheduling pipeline that spans forecasting to real time [\[16\]](#ref-16). Each stage writes records. A mission states a tracking requirement and a requested activity; the requested activity is negotiated against competing requests; a negotiated allocation is produced; and an executed pass, or a failure to execute, is recorded against the allocation. The logs are exposed to users and analysts through the DSN service catalog and through the SPS schedule archives, which are the operational interfaces of the scheduling system rather than research artifacts. The provenance is therefore the machinery of operations itself: these are not survey data collected for study but transaction records generated by the act of scheduling.

**Native unit and fields.** The native unit of the scheduling and tracking logs is the requested tracking activity. A single record documents one requested activity and carries, in the operational schema, the requesting mission, the requested antenna or antenna class, the requested time window, the requested frequency band, the activity type (telemetry downlink, command uplink, or radiometric tracking), the negotiated allocation if one was reached, and the executed pass if one occurred. This native unit maps almost directly onto the dissertation's primary unit of analysis, the tracking-pass request, which is the single most important reason the design is feasible on existing data: the record the network keeps is the record the analysis needs, requiring transformation rather than new instrumentation.

**Coverage.** The intended coverage is a multi-year span of the request and tracking logs, long enough to include several cycles of the recurring high-contention windows and a representative set of mission phases across mission classes. The multi-year requirement is not a convenience; it is a statistical necessity dictated by the hypotheses. A heavy upper tail can be fitted only if the tail is observed often enough, and a concentration onto a minority of windows can be estimated only if those windows recur enough times to be distinguished from sampling noise. A short record undersamples the tail and the carrying windows, which is precisely the failure mode the design exists to avoid; the coverage requirement is the data-side expression of Taleb's warning that short records systematically understate the worst realizations.

**Characteristic biases.** Three biases inhere in the scheduling and tracking logs by their nature as operational records. The first and most consequential is strategic mission behavior: because the schedule can shorten or drop a request, missions submit early and inflate requested durations to hedge, so the requested-time field overstates true need and the request stream is a hedged quantity rather than a clean demand signal. The second is a definitional ambiguity in the executed-pass field: a pass may be executed fully, reduced, or dropped, and the boundary between a reduced-but-useful pass and a reduced-below-usefulness pass is a modeling choice not recorded in the log. The third is instrumentation noise in the execution record itself, since the same metrology infrastructure that times and validates antenna operations can register disturbances unrelated to scheduling; machine-learning work on detecting DSN antenna motions from metrology data illustrates that the raw operational signal carries movement and disturbance artifacts that must be distinguished from scheduled activity [\[36\]](#ref-36). Each bias is carried forward into Section 4.4 (variable construction) and Section 4.6 (limitations) with an explicit handling rule.

### 4.2.2 NTRS DSN loading and forecasting reports

**Provenance.** The second named source is the corpus of DSN loading analyses, traffic-forecasting studies, and capacity assessments hosted on the NASA Technical Reports Server. These reports are produced by JPL in support of NASA's Space Communications and Navigation program and its systems-engineering office, which periodically model and analyze projected future-mission demand on the DSN; the most recent such study models demand out to a thirty-year horizon and reports the resulting capacity, spectrum, capability, and loading trends [\[31\]](#ref-31), and an earlier study in the same line models the traffic that the human-exploration era will add [\[17\]](#ref-17). The expansion analyses that quantify the gap between a specific science portfolio's projected demand and current supply belong to the same provenance [\[18\]](#ref-18). These are deliberative analytical products presented to program leadership for strategic and programmatic decisions, not transaction logs.
**Native unit and fields.** The native unit of the NTRS reports is the aggregate: loading by complex, by band, and by epoch, and projected demand by mission class over a planning horizon. The reports do not expose individual requests; they expose summaries and projections. Their value to this design is therefore not as a primary source of request-level events but as a validated context against which the log-derived aggregates can be checked. If the load covariate computed from the request logs over a given interval and complex disagrees with the loading reported for that interval and complex in an NTRS study, that disagreement is a measurement-error signal to be investigated before estimation, not a finding.

**Coverage.** The NTRS reports collectively cover the network's loading history and its forward projections, with individual studies pinned to particular epochs and portfolios. Their coverage is broad in time and coarse in unit, the exact complement of the scheduling logs (narrow in unit, dependent on access for time coverage). The two coverages are designed in this study to cross-check each other.

**Characteristic biases.** The principal bias of the NTRS reports is that the forward-looking studies are projections built on assumptions about future mission mix and data rates, so their numbers are conditional forecasts rather than observed loads; they validate the historical load covariate well and the projected load covariate only as far as their assumptions hold. A secondary consideration is that these reports are authored to inform strategic decisions and therefore emphasize trends and implications over the dispersion within an aggregate, so they confirm the existence and growth of oversubscription (the proposition that the problem is real and material) without themselves answering the distributional question. That confirmation is the role assigned to them here.

### 4.2.3 Mission downlink-requirement records

**Provenance.** The third named source is the set of per-mission downlink-requirement records and critical-event windows, maintained in mission service agreements and reflected in the request stream. Each supported mission carries a stated data-return requirement and a set of phases during which tracking is mission-critical: launch, trajectory-correction maneuvers, planetary encounters, and entry-descent-and-landing sequences. These records are the provenance of the mission-phase covariate and of the criticality weights used in the construct-validity robustness analysis.

**Native unit and fields.** The native unit is the mission, or more precisely the mission-phase: a record states, for a mission, its nominal data rate, its aggregate data-return requirement, and the calendar windows of its critical events. The historical antenna-extension and modernization record provides the link-margin and aperture context that connects a mission's nominal data rate to the antenna class it must use [\[74\]](#ref-74), [\[75\]](#ref-75). This matters because the lost-downlink magnitude depends on the data rate that the requested band and antenna class would have supported.

**Coverage.** Coverage of the mission records is the most access-dependent of the three sources and, per the evidence-gap flag carried from the expansion plan, the least documented in the public literature. No public citation fully documents per-mission critical-event windows; the records are obtained from mission service agreements rather than from a published catalog. The consequence is that the mission-phase covariate is feasible to construct for missions whose agreements are accessible and that the criticality-weighted construct may be only partially feasible, a limitation stated plainly in Section 4.6 and revisited in the construct-validity discussion.

**Characteristic biases.** The mission records inherit the same strategic-behavior bias as the request log, because a mission's stated requirement and declared criticality are partly negotiating positions: a mission has an incentive to declare more phases critical and to state a generous data-return requirement. The criticality weighting must therefore be treated as a mission-declared quantity, not an objective science-value measure, and the construct-validity analysis reports results both unweighted (data-volume units) and weighted (criticality units) precisely so that the declared-criticality bias is exposed rather than buried.

## 4.3 Units of analysis

The design uses two units of analysis, a primary and a secondary, and the distinction between them carries weight because the two hypotheses about the shape of the penalty are tested at different levels of aggregation.

### 4.3.1 Primary unit: the tracking-pass request

The primary unit of analysis is the tracking-pass request, defined as one requested activity for one mission on one antenna class over one viewing window. This is the unit at which wait time is defined (the elapsed time from the request's submission to its allocation or expiry), at which the pass-loss indicator is defined (whether this requested activity was executed, reduced, or dropped), and at which the survival model and the pass-loss regression of Chapter 5 operate. The choice of the request, rather than the mission or the pass, as the primary unit is deliberate: the hypotheses concern the distribution of waits and losses across requests, and only a request-level unit exposes that distribution. Aggregating to the mission would average away the within-mission variation that the identification strategy depends on, and aggregating to the executed pass would discard the dropped requests, which are the events the analysis most needs to observe.

### 4.3.2 Secondary unit: the geometry-phase window

The secondary unit of analysis is the geometry-phase window, defined as a discretized cell formed by the cross of an orbital-geometry condition, a mission phase, a complex, and a band. Lost downlink is aggregated to this cell to test the concentration clause of the hypothesis: the Gini coefficient of lost downlink across windows and the share of total loss carried by the top decile of windows are both computed over the geometry-phase window as the unit. The window is the natural unit for concentration because the alternative hypothesis is precisely that a minority of structurally identifiable windows carries a majority of the loss, and a window must be defined as a structural cell, not as a request, for that claim to be testable. The discretization of continuous geometry covariates into window cells is itself a measurement choice (the bin boundaries of declination, of viewing-window overlap, and of the load axis), and Section 4.5 specifies that this discretization is varied in sensitivity analysis so that the concentration result is not an artifact of an arbitrary binning.

## 4.4 Variable construction and the measurement table

This section operationalizes every construct the hypotheses require, carrying forward and elaborating the variable definitions fixed in the prospectus and in Chapter 1. Each construct is defined by its operational rule, its source record, its scale, and its characteristic measurement error. The notation is the one fixed in Chapter 1: \(W_i\) is the wait time of request *i*, \(c_i\) its censoring indicator, \(L_i\) its pass-loss indicator, \(D_w\) the lost downlink aggregated to window *w*, and \(X\) the covariate vector.

### 4.4.1 Wait time (W)

Wait time is the elapsed time from the moment a request is submitted to the moment of its confirmed allocation. It is the time-to-event outcome of the survival model and is right-censored: for a request still pending at the observation cutoff, and for a request whose viewing window expires before any allocation, the event (allocation) is not observed, and the censoring indicator \(c_i\) records this. The distinction between the two censoring routes matters and is preserved: a pending request is conventionally right-censored at the cutoff, whereas an expired request is a competing-risk event (the window closes, foreclosing allocation) and is handled as such rather than treated as ordinary censoring, because treating an expiry as if the request were merely still waiting would bias the survival estimate [\[64\]](#ref-64). The operational rule is therefore: \(W_i\) equals (allocation timestamp minus submission timestamp) when allocation occurs; \(c_i\) equals one with the request right-censored at the cutoff when the request is still pending; and the expiry is recorded as a competing event with its own time when the window closes unserved. The measurement error in \(W_i\) is small relative to the other constructs because both timestamps are recorded by the scheduling system, but the submission timestamp is contaminated by strategic early submission: a mission that submits a week early to hedge inflates \(W_i\) not because the network was slow but because the mission chose to wait, and this is the wait-time analogue of the hedged-request bias.

### 4.4.2 Pass-loss indicator (L)

The pass-loss indicator \(L_i\) is binary, set to one when a requested pass is not executed as requested (dropped, expired, or reduced below a science-useful threshold) and zero when executed as requested. The construct's difficulty is entirely in the word "reduced": a fully dropped pass and a fully executed pass are unambiguous in the log, but a shortened pass requires a science-usefulness threshold to classify, and that threshold is a modeling choice rather than a logged fact. The operational rule fixes a primary threshold (a requested-duration fraction below which a reduced pass is counted as lost) and then varies that threshold across a pre-specified range in sensitivity analysis, so that the pass-loss result is reported as a function of the threshold rather than as a single number contingent on an arbitrary cut. This sensitivity treatment is the handling rule for the second characteristic bias of the scheduling log named in Section 4.2.1. The measurement error in \(L_i\) is thus concentrated in the reduced-pass region and is addressed by transparency about the threshold rather than by pretending the boundary is sharp.

### 4.4.3 Lost-downlink magnitude (D)

The lost-downlink magnitude is the shortfall between the requested data return and the executed data return for a lost or reduced pass, computed from the requested band, the requested duration, and the mission's nominal data rate. It is the science-throughput penalty in physical (bit-volume) units and is the quantity aggregated to the geometry-phase window as \(D_w\) for the concentration test. The operational rule multiplies the unserved fraction of the requested duration by the nominal data rate that the requested band and antenna class would have supported, drawing the data rate from the mission downlink-requirement record. Two measurement errors enter here and are stated rather than hidden. First, the nominal data rate varies with link conditions (range, elevation, weather, antenna performance), so the realized rate during an executed pass would differ from the nominal rate used in the computation, introducing error in the dependent variable; the historical link-margin and aperture record [\[74\]](#ref-74), [\[75\]](#ref-75) and the future-trends analysis of rising data rates [\[31\]](#ref-31) document that this variation is real and growing. Second, the construct equates lost bits with lost science, which is a construct-validity simplification addressed in Section 4.4.7. The handling rule for the data-rate error is to propagate it as measurement error in the dependent variable and to report the lost-downlink result under a band of nominal-rate assumptions rather than a single point rate.

### 4.4.4 Orbital-geometry covariates

The orbital-geometry covariates operationalize the structural conditions under which a request's viewing window is generous or compressed. They comprise the target declination, the viewing-window overlap among concurrently supported targets, the elevation profile at each complex, and the conjunction or occultation conditions that compress the usable window. The operational rule derives these from the requested target and time window using standard ephemeris geometry, so that, unlike the request fields, they are not contaminated by mission strategic behavior: the geometry of a target's viewing window is set by celestial mechanics and is not chosen by the mission. This behavior-independence is the property that makes the geometry covariates usable as a robustness instrument in Chapter 5, because geometry-driven window compression varies a request's contention without being a product of the mission's own padding. The measurement error in the geometry covariates is the smallest of any construct, limited to ephemeris precision and to the discretization of continuous geometry into window bins.

### 4.4.5 Frequency band
The band is the requested frequency band (for example S, X, or Ka), which governs antenna eligibility and contention with other band users. The DSN's antennas are outfitted for specific bands, and the radio-astronomy and receiving-system literature documents which bands the large apertures support and how receiving systems are configured across the complexes [\[34\]](#ref-34). The operational rule reads the band directly from the request record; its measurement error is negligible because the band is a categorical operational fact. Band matters to the design because contention is band-specific. A request competes not against all requests at a complex but against requests eligible for the same band, so the concurrent-load covariate is computed within band.

### 4.4.6 Concurrent-mission load

The concurrent-mission load is the count and aggregate requested antenna-time of other missions contending for the same complex and band in the same interval. It is the realized load covariate that operationalizes the inflow-shape variable of the Forrester mechanism: the alternative hypothesis predicts that loss concentrates where many missions' locally optimal requests collide, and the concurrent-load covariate is the measured collision intensity. The operational rule computes, for each request, the number and the aggregate requested antenna-time of competing requests overlapping its window on its complex and band. Two features of this construct require care. First, because it is built from requested (not executed) antenna-time, it inherits the hedged-request bias: padded requests inflate the measured load, so the load covariate measures hedged contention, not physical contention. Second, the load is time-varying over the life of a waiting request, since competitors arrive and depart while the request waits, and the survival model therefore admits the load as a time-varying covariate (the time-dependent-covariate extension of the Cox model). The handling rule for the hedging bias is the cross-check against the NTRS loading reports (Section 4.2.2): the log-derived load is validated against the independently reported aggregate load for the same complex and epoch, and a systematic gap is read as the hedging margin rather than as physical load.

### 4.4.7 Mission-phase window

The mission-phase indicator is a categorical covariate marking whether a request falls in a critical phase (launch, maneuver, encounter, entry-descent-and-landing) or in routine cruise. It is drawn from the mission downlink-requirement record and is the covariate through which the navigation-and-guidance stakes enter the measurement: a tracking pass lost in a critical phase degrades orbit determination at the moment it matters most, so the mission-phase window is the construct that lets the concentration analysis distinguish high-consequence losses from routine ones. The operational rule classifies each request by the mission-phase window in which its time falls, using the critical-event calendar from the mission record. The measurement error is the declared-criticality bias of Section 4.2.3: a mission may declare more phases critical than an objective measure would, so the criticality-weighted construct is reported alongside the unweighted one. This is also the construct-validity handling for the lost-downlink simplification. Because not all bits carry equal scientific value and a navigation-critical tracking pass has a value not captured by a data-volume measure, the lost downlink is reported both in raw data-volume units and, where mission records permit, weighted by mission-declared criticality, so that the navigation-critical losses are not averaged into invisibility.

### 4.4.8 The measurement table

The following table (Table 4.1) is the codebook for the design. Each row states a construct, its operational definition, its source record, and its scale. It is the consolidated reference for Chapters 5 and 6, which estimate over exactly these constructs.

**Table 4.1. Measurement codebook.**

| Construct | Operational definition | Source record | Scale |
|-----------|------------------------|---------------|-------|
| Wait time \(W_i\) | Allocation timestamp minus submission timestamp; right-censored if pending at cutoff; expiry recorded as competing event | DSN scheduling/tracking logs (SPS archives, service catalog) | Continuous, non-negative (time) |
| Censoring indicator \(c_i\) | 1 if request pending at observation cutoff (right-censored); 0 if allocation observed; expiry flagged separately as competing risk | DSN scheduling/tracking logs | Binary, plus competing-risk flag |
| Pass-loss indicator \(L_i\) | 1 if requested pass dropped, expired, or reduced below science-usefulness threshold; 0 if executed as requested; threshold varied in sensitivity analysis | DSN scheduling/tracking logs | Binary (threshold-parameterized) |
| Lost-downlink magnitude \(D\) | (Unserved fraction of requested duration) x (nominal data rate for requested band and antenna class); aggregated to window as \(D_w\) | Scheduling logs x mission downlink-requirement records | Continuous, non-negative (bit volume); optionally criticality-weighted |
| Target declination | Ephemeris declination of requested target over the requested window | Derived from request target/window via ephemeris | Continuous (degrees) |
| Viewing-window overlap | Degree of overlap among concurrently supported targets' viewing windows | Derived from ephemeris geometry | Continuous (overlap fraction) |
| Elevation profile | Elevation of target at each complex over the window | Derived from ephemeris geometry | Continuous (degrees) |
| Conjunction/occultation compression | Indicator and magnitude of window compression from conjunction or occultation | Derived from ephemeris geometry | Continuous / binary |
| Band | Requested frequency band (S, X, Ka, ...) | DSN scheduling/tracking logs | Categorical |
| Concurrent-mission load | Count and aggregate requested antenna-time of competing requests on same complex and band overlapping the window; time-varying | DSN scheduling/tracking logs; cross-checked vs NTRS loading | Continuous (count; antenna-hours), time-varying |
| Mission-phase window | Critical phase (launch / maneuver / encounter / EDL) vs cruise, by request time | Mission downlink-requirement records (service agreements) | Categorical |
| Criticality weight | Mission-declared criticality of the phase, used to weight \(D\) | Mission downlink-requirement records | Ordinal / continuous weight |
| Geometry-phase window (unit) | Discretized cell {geometry condition x mission phase x complex x band}; unit of concentration aggregation | Constructed from above | Categorical cell |

Two properties of the table are worth making explicit. First, the constructs partition cleanly by their vulnerability to strategic behavior: the wait time, the pass-loss indicator, the lost-downlink magnitude, and the concurrent load are all derived from request fields and therefore inherit the hedging bias, whereas the geometry covariates are derived from ephemeris and are behavior-independent. This partition is what the identification strategy of Chapter 5 exploits, using the behavior-independent geometry as a robustness instrument against the behavior-contaminated request fields. Second, the lost-downlink magnitude is the only construct built by combining two source records, the scheduling log and the mission record, and is therefore the construct most exposed to the access constraints on the mission records; its feasibility is the most access-dependent element of the design.

## 4.5 Coverage requirement and panel assembly

### 4.5.1 Why multi-year coverage is mandatory

The coverage requirement is not a parameter to be optimized but a precondition imposed by the hypotheses. The wait-time-tail clause asks whether the upper tail of the wait distribution is heavy, and a heavy tail is, by definition, a region of rare-but-large values; it can be fitted only from a record long enough to contain enough tail observations to distinguish a power-law or generalized-Pareto upper tail from an exponential one [\[4\]](#ref-4). The concentration clause asks whether a minority of windows carries a majority of the loss, and a window's loss can be estimated only if the window recurs enough times across the record to separate its carrying share from sampling variation; the small-sample bias of concentration measures such as the Gini coefficient is well documented and is downward in small populations [\[77\]](#ref-77), so a thin record would bias the concentration measure toward the uniform null and could manufacture a false retention of H0. The multi-year coverage requirement is therefore the data-side enforcement of the statistical-conclusion-validity discipline: it is the condition under which the tail and the concentration are observable rather than washed out by sampling noise. The requirement is to span several cycles of the recurring high-contention windows and a representative set of mission phases across mission classes, so that both the tail and the carrying windows are sampled often enough to fit.

### 4.5.2 Panel assembly

The measured panel is assembled by joining the three sources at the request level. The scheduling and tracking logs supply one row per requested activity with its timestamps, allocation, execution, band, and antenna class. The mission downlink-requirement records supply, by mission and phase, the nominal data rate and the critical-event calendar, joined onto each request by mission and time to produce the lost-downlink magnitude, the mission-phase indicator, and the criticality weight. The geometry covariates are computed from the requested target and window and joined onto each request. The product is a request-level panel carrying, for each request, the wait time, the censoring indicator, the pass-loss indicator, the lost-downlink magnitude, and the full covariate vector. A second, derived table aggregates lost downlink onto the geometry-phase windows for the concentration analysis. The discretization that defines the windows (the bin boundaries on declination, overlap, elevation, and the load axis, and the phase categories) is specified before estimation and then varied in sensitivity analysis, so that the concentration result is reported as robust to the binning rather than as contingent on one arbitrary cut. This is the panel that Chapter 6's five pre-registered estimation steps consume.

### 4.5.3 Reconstruction where raw access is constrained

Where direct access to the raw request logs is constrained for some intervals (Section 4.7), the design does not simply discard those intervals, because doing so would bias the coverage toward the accessible epochs and could distort the tail and concentration estimates. Instead, the published NTRS loading reports provide aggregate cross-checks sufficient to calibrate the load covariate for the constrained intervals, and, where an interval is represented in the literature only by reported summaries or published survival-style curves, the data can be partially reconstructed using the established methodology for recovering individual time-to-event data from published Kaplan-Meier curves and reported at-risk counts [\[88\]](#ref-88). This reconstruction is a fallback, not a primary method: it recovers an approximation of the request-level panel from aggregate or summary publications when the raw log is unavailable, and any interval so reconstructed is flagged in the panel and its sensitivity to the reconstruction is reported. The handling rule is that reconstructed intervals are analyzed both included and excluded, so that the contribution does not rest on the reconstructed approximation.

## 4.6 Data-quality and measurement limitations

Four measurement limitations are recognized at the design stage, each tied to a specific construct and each carried into the threats-to-validity discussion of Chapter 5. Stating them here, at the point of measurement, is the discipline that keeps the eventual empirical claim honestly bounded.

### 4.6.1 Strategic padding contaminates requested time

The first and most consequential limitation is that request records reflect strategic mission behavior. Because the schedule can shorten or drop a request, missions inflate requested durations and submit early to hedge, so requested time overstates true need and must be read as a hedged quantity, not a clean demand signal. This contaminates the wait time (early submission inflates \(W_i\)), the concurrent-load covariate (padded requests inflate measured load), and, through the load, the pass-loss and lost-downlink constructs. The mechanism by which this bias would distort the result is concrete: hedging manufactures apparent contention out of strategic asking, so a naive analysis could find concentration where there is only coordinated padding. The handling is threefold: the request is treated throughout as a strategic artifact rather than a demand statement; the geometry covariates, which are behavior-independent, are used as a robustness instrument that varies contention without being a product of padding; and the log-derived load is cross-checked against the independently reported NTRS aggregate load, with a systematic gap read as the hedging margin. The bias is real and is the reason the geometry instrument exists; it does not defeat the design but it bounds the strength of any claim that rests on request-derived constructs alone.

### 4.6.2 The science-usefulness threshold for reduced passes

The second limitation is that reduced (not fully dropped) passes require a science-usefulness threshold to classify as lost or not lost, and that threshold is a modeling choice rather than a logged fact. A reduced pass that returns most of its requested data is arguably executed; a reduced pass that returns a fraction is arguably lost; the boundary is continuous and the log does not draw it. The mechanism of distortion is that a threshold set too generously would count borderline-useful passes as losses and inflate the apparent penalty, while a threshold set too strictly would suppress it. The handling is to fix a primary threshold, vary it across a pre-specified range, and report the pass-loss and lost-downlink results as functions of the threshold, so that the contribution's dependence on the threshold is visible rather than concealed in a single number.

### 4.6.3 Data-rate uncertainty in the dependent variable

The third limitation is that the lost-downlink magnitude depends on assumed nominal data rates that vary with link conditions, introducing measurement error in the dependent variable. The realized data rate during a pass depends on range, elevation, weather, and antenna performance, none of which is fully captured by the nominal rate used to compute the shortfall, and the future-trends analysis documents that data rates are rising and diversifying, which widens this uncertainty over the coverage span [\[31\]](#ref-31). The mechanism of distortion is classical measurement error in the outcome, which inflates the variance of the lost-downlink estimates and, if the error is correlated with band or geometry, could bias the concentration. The handling is to propagate the rate uncertainty by reporting lost downlink under a band of nominal-rate assumptions rather than a single rate, and to check whether the concentration result is stable across that band.
### 4.6.4 Access-constrained intervals coarsen the load covariate

The fourth limitation is that access constraints on the raw logs may force reliance on aggregated loading reports for some intervals, which coarsens the load covariate from a request-level measure to an interval-level aggregate. The distortion runs through a loss of within-interval variation. An interval represented only by its aggregate load cannot distinguish the requests within it that faced high momentary contention from those that faced low contention, and the load coefficient attenuates toward zero for those intervals. The handling is the reconstruction-and-flagging rule of Section 4.5.3, the included-and-excluded sensitivity analysis for reconstructed intervals, and the explicit reporting of which intervals are request-level and which are aggregate-only, so that the coarsening is a labeled property of the panel rather than a hidden one.

### 4.6.5 The mission-record gap

Beyond the four prospectus limitations, the chapter records a fifth, flagged in the expansion plan as the most access-dependent input. The mission downlink-requirement records and criticality weights are the least-sourced dataset, and no public citation fully documents per-mission critical-event windows. The consequence is that the mission-phase covariate and the criticality-weighted construct are feasible only for missions whose service agreements are accessible, and the criticality weighting may be only partially feasible across the portfolio. The handling is to report the core results, the wait-time tail and the data-volume concentration, without the criticality weighting, so that the central contribution does not depend on the least-available data, and to present the criticality-weighted results as a robustness extension wherever the mission records permit, clearly marked as covering a subset of missions.

## 4.7 Access, data-use arrangements, and ethics

### 4.7.1 Access paths

The three sources are accessed through three different paths, and the difference in access difficulty is itself a design consideration. The DSN scheduling and tracking logs are accessed through the DSN service-catalog and SPS schedule-archive interfaces under the appropriate data-use arrangements. These are operational interfaces, and access is governed by the arrangements under which a researcher is granted entry to operational scheduling data. The NTRS loading and forecasting reports are publicly retrievable from the NASA Technical Reports Server, requiring no special arrangement; they are the most freely accessible of the three and are for that reason assigned the cross-check role rather than the primary-event role. The mission downlink-requirement records are obtained from mission service agreements, which are the most access-restricted of the three and which underlie the mission-record gap of Section 4.6.5. The access asymmetry across the three sources is the practical reason the design is structured so that its central claim rests on the scheduling logs cross-checked against the public NTRS reports, with the access-restricted mission records carrying only the robustness extensions.

### 4.7.2 Data-use arrangements and provenance discipline

Access to operational DSN scheduling data is conditioned on data-use arrangements, and the design respects those arrangements as a boundary rather than treating the logs as open data. The provenance discipline is twofold. First, the logs are operational records, so the analysis treats them as a sample of how the network actually allocated time, not as a controlled experiment; the identification strategy of Chapter 5 is built around this observational character. Second, any interval whose data are reconstructed from published summaries rather than retrieved from the raw archive is flagged so that the provenance of every panel row is traceable, and the included-and-excluded sensitivity analysis ensures that the contribution can be evaluated on the raw-access subset alone. This is the discipline that keeps the residual risk manageable: the panel's provenance is explicit, and the central claim is reproducible on the subset whose provenance is cleanest.

### 4.7.3 Ethics and sensitivity

The ethics of this data are not the ethics of human-subjects research; the records concern spacecraft, antennas, and schedules, not persons, so the standard human-subjects considerations do not apply. Two genuine ethical considerations do apply and are addressed. The first is institutional sensitivity. The request and allocation records reveal which missions were cut, when, and by how much, and a distributional finding that localizes the carrying windows necessarily identifies the conditions under which particular mission classes lose time. The handling is to report results at the level of structural windows (geometry, phase, band, complex, concurrency) rather than as a ranking of named missions by loss, so that the contribution localizes the carrying conditions without producing a public scoreboard of mission winners and losers; where mission identity is needed for the mission fixed effects of Chapter 5, it is used as an absorbed control rather than reported as a finding. The second is the obligation of accurate representation under access constraint. Because some intervals may be reconstructed or aggregate-only, the design is bound to represent the provenance and reliability of each part of the panel accurately rather than presenting a uniform-quality dataset, which is the data-integrity counterpart of the design-stage honesty that governs the whole dissertation.

### 4.7.4 Reproducibility and the design-stage status

The reproducibility commitment is that the measurement plan specified here, the operational rules, the source records, the scales, the thresholds, the binning, and the validation checks, is fixed before any estimation, so that the eventual analysis is a pre-registered application of this codebook rather than a search over specifications. This pre-registration of measurement is the data-side complement to the pre-registered decision rules of Chapter 6, and together they guard against the post-hoc threshold selection and specification mining that heavy-tail and concentration analyses are prone to. The status of the chapter is restated to close it: no log has been retrieved, no construct has been computed, and the codebook is a plan. Its value is that it converts each operational record into a measured construct with a defined scale and a named bias before the first estimation, so that when the design is run the measurements are disciplined rather than improvised.

## 4.8 Validation against known values

A measurement plan that cannot be checked against an independent value is a plan that cannot detect its own errors. The design therefore builds three validation checks, each comparing a log-derived measure against an independently reported quantity, and each specified before estimation so that a disagreement is a diagnostic signal rather than a post-hoc adjustment.

### 4.8.1 Load validation against NTRS reports

The first and primary validation compares the concurrent-mission load computed from the request logs against the loading reported, for the same complex, band, and epoch, in the NTRS loading and forecasting studies [\[17\]](#ref-17), [\[31\]](#ref-31), [\[18\]](#ref-18). The two are computed from different vantage points: the log-derived load is built bottom-up from individual requests, while the NTRS load is reported top-down as an aggregate. Agreement between them validates the bottom-up construction; a systematic gap is interpreted, as Section 4.4.6 specifies, as the hedging margin (the amount by which requested load exceeds the load the reports treat as real), which is itself an informative quantity rather than merely an error. This validation anchors the load covariate's credibility and is the reason the publicly accessible NTRS reports are an integral part of the design rather than mere background.

### 4.8.2 Loss validation against documented oversubscription

The second validation checks the aggregate pass-loss rate derived from the logs against the oversubscription documented in the optimization literature, which calibrates its methods on real DSN demand in which requests provably exceed capacity and a subset of activities must be excluded [\[33\]](#ref-33), [\[32\]](#ref-32). The check is directional and order-of-magnitude rather than exact, because the optimization studies report on particular benchmark instances rather than the full multi-year panel, but it confirms that the log-derived loss rate is consistent with the independently documented fact that the network is oversubscribed. A log-derived loss rate near zero, or implausibly high, would signal a parsing or classification error in the pass-loss construct and would halt the analysis for diagnosis. This is the validation of the proposition that the problem is real: the measured loss must be consistent with the documented oversubscription before any distributional claim about that loss is credible.

### 4.8.3 Data-rate validation against link-margin and trends records

The third validation checks the nominal data rates used in the lost-downlink computation against the link-margin and aperture record and the documented data-rate trends. The historical antenna-extension record establishes the link margins that the large apertures provide [\[74\]](#ref-74), the modernization and calibration record documents the receiving-system context [\[75\]](#ref-75), [\[34\]](#ref-34), and the future-trends analysis documents the magnitude and direction of data-rate growth [\[31\]](#ref-31). The check confirms that the nominal rates assigned to each band and antenna class fall within the physically documented ranges; a rate outside the documented range would signal an error in the mission-record join. Because this validation bounds the dependent variable, it is the most consequential for the lost-downlink magnitude and is run under the same band of nominal-rate assumptions described in Section 4.6.3.

### 4.8.4 What the validations can and cannot establish

The three validations can establish that the log-derived constructs are consistent with independently reported aggregates, which is a necessary condition for the panel to be trustworthy. They cannot establish the distributional claim itself, because the independently reported quantities are aggregates and the contribution is precisely about the distribution that the aggregates conceal; no NTRS report or optimization benchmark publishes the realized wait-time tail or the loss concentration, which is the gap the dissertation fills. The validations therefore certify the measurement, not the finding: they confirm that the panel's aggregates match the literature's aggregates, leaving the distributional question to the estimation. Confidence in the constructs, after these validations would be run, is best characterized as moderate-to-high for the constructs derived from the scheduling logs and validated against NTRS, and lower for the criticality-weighted construct that depends on the least-available mission records. That graded confidence is carried into Chapter 5, where the estimators are matched to the constructs and the threats to validity are addressed in full.

## 4.9 Summary

The prospectus data section has been carried forward here into a full measurement specification. The three datasets, the DSN scheduling and tracking logs, the NTRS loading and forecasting reports, and the mission downlink-requirement records, have been described for provenance, native unit, coverage, access path, and characteristic biases. The two units of analysis are fixed: the tracking-pass request for the wait and pass-loss distributions, and the geometry-phase window for the concentration aggregation. Every construct the hypotheses require has been operationalized, wait time with its competing-risk censoring, the pass-loss indicator with its threshold parameterization, the lost-downlink magnitude with its data-rate uncertainty, and the orbital-geometry, band, concurrent-load, and mission-phase covariates, and the resulting codebook serves as the reference for the estimation chapters. The chapter has established why multi-year coverage is a statistical necessity rather than a convenience, specified the panel assembly and the reconstruction fallback for access-constrained intervals, and enumerated five data-quality limitations, each tied to a construct and each given a handling rule. It has set out the access paths, data-use arrangements, and ethics, distinguishing the freely accessible NTRS reports from the access-restricted mission records and structuring the design so that the central claim rests on the best-accessible and best-validated data. Three validation checks against independently reported values, each fixed before estimation, complete the specification. The central measurement claim is the one stated at the outset: the request log is a hedged, strategic artifact rather than a clean demand signal, and the entire apparatus is built to measure the tail and the concentration the mechanism predicts, not the artifacts of how missions ask for time. The chapter's status is design-stage throughout: the datasets are real and the access paths are real, but no log has been analyzed, and every statement about realized values remains the empirical question the design specified in the chapters that follow is built to answer.
# Chapter 5: Research Design and Identification

## 5.0 The chapter's answer

The distributional question posed by the hypotheses, whether the Deep Space Network science-throughput penalty is uniform (H0) or heavy-tailed and concentrated (H1), is identifiable from the realized scheduling and tracking logs with a three-estimator design whose validity rests on assumptions that are stated formally, are partly testable, and are bounded where they are not testable. The design turns on a deliberate division of labor between two kinds of inference. The first is descriptive. The shape of the wait-time distribution and the concentration of lost downlink across geometry-phase windows are properties of the realized record, and characterizing them requires only that the record be complete and that the estimators of tail behavior and concentration be applied with their pre-registered safeguards. This descriptive inference carries no exogeneity assumption, and the chapter is explicit on that point. The second kind is causal-adjacent: the conditional association between pass-loss and its drivers, orbital geometry, frequency band, and concurrent-mission load, holding mission and epoch fixed, requires a stated identifying assumption; that assumption is argued, its threats enumerated, and a behavior-free robustness lever (geometry-driven viewing-window compression, set by celestial mechanics rather than by mission choice) introduced to relieve the part of the assumption that is least credible.

This division matters because the contribution stands or falls on two separable inferential claims, and conflating them would be the design's most consequential error. The concentration result, if it holds, is the more secure of the two, because it rests on the completeness of the log rather than on an identification claim about why the concentration arises. The driver regression is the more fragile, because requested antenna time is plausibly endogenous to expected contention. A design that earned the strong concentration result but oversold the fragile driver result would mislead the very capacity-planning and scheduling-policy decisions the dissertation is meant to inform. The architecture here is therefore an architecture of honesty about which claim is load-bearing for which conclusion. Estimands are defined first (5.1), so that every later choice is traceable to a target quantity rather than to a method preference. Estimators are then matched to the estimands (5.2), with the rationale for each choice argued rather than asserted. Identification is treated as its own section (5.3), separating the descriptive estimands from the conditional one. Specifications are written out (5.4). Threats to validity are enumerated across all four Cook-and-Campbell categories with a named mitigation for each (5.5). The robustness battery, the power and minimum-detectable-effect analysis, the pre-registration commitment, and the computational plan follow (5.6 through 5.9). The confidence posture inherited from the proposal is preserved throughout: the mechanism that predicts H1 is theoretically well-supported, but whether H1 holds on the real logs is untested and explicitly so, and no number in this chapter is an executed estimate.

The problem frame is the same one the proposal used. The current state is that the operational and optimization literature reports the residual scheduling penalty, when it reports it at all, as an aggregate satisfaction rate, a mean. The desired state is a research design that recovers the distributional shape behind that mean, separating the tail-behavior question from the concentration question from the driver question, each with a matched estimator and a stated assumption set. The gap is that no design in the reviewed literature does this for ground-station scheduling: survival analysis, heavy-tail estimation, and concentration measurement are each mature in their home disciplines, but their joint application to the DSN request stream, with the identification care that the endogeneity of requested time demands, has not been specified. Leaving the gap open has a consequence. The choice between broad and targeted remediation continues to be made without a defensible characterization of the penalty's shape, and any future attempt to measure that shape risks doing so with an estimator-assumption mismatch that the present design is built to avoid.

## 5.1 Estimands

The design targets three estimands, defined here before any estimator is named so that the matching in Section 5.2 is visibly driven by the target quantity. Each estimand is stated in the fixed notation of Chapter 1: \(W_i\) is the wait time of request \(i\) with censoring indicator \(c_i\); \(L_i\) is the pass-loss indicator; \(D_w\) is lost downlink aggregated to geometry-phase window \(w\); \(X\) is the covariate vector (orbital geometry, band, concurrent load, mission phase); \(\mu_m\) and \(\lambda_t\) are mission and epoch fixed effects.

The first estimand is the **shape of the wait-time distribution**, and specifically whether the upper tail of \(W\) is heavy in the precise sense that a heavier-than-exponential family fits the tail better than the exponential null benchmark. This is a property of the marginal (and, in stratified form, conditional) distribution of \(W\), and the quantity of interest is the tail index: in the generalized-Pareto parameterization the shape parameter \(\xi\), where `xi > 0` is the formal signature of a heavy (Pareto-type) tail and `xi <= 0` is consistent with the light-tailed null. The estimand is not a single point but the pair (tail family verdict, tail-index estimate with uncertainty), because the hypothesis is about family membership (heavy versus light) and the operational decision depends on how heavy.

The second estimand is the **shape and concentration of the lost-downlink distribution** across geometry-phase windows. Two summaries operationalize it, both fixed in Chapter 1: the Gini coefficient \(G\) of \(D_w\) across windows, and \(T_{10}\), the share of total lost downlink carried by the top decile of windows ranked by loss. The uniformity null predicts \(G\) near zero and \(T_{10}\) near 0.10; the concentration alternative predicts elevated \(G\) and \(T_{10}\) materially above 0.10. The estimand here is descriptive by construction: it is a feature of the realized loss record aggregated to windows, and it makes no claim about why the loss concentrates, only whether it does.

The third estimand is the **conditional association between pass-loss and its drivers**, the partial relationship between \(L\) (and, for magnitude, \(D\)) and the geometry, band, and concurrent-load components of \(X\), holding mission and epoch fixed through \(\mu_m\) and \(\lambda_t\). This is the only estimand that carries a causal flavor, because the policy reading of the result ("higher concurrent load raises loss probability in the contested band") presumes that the load coefficient reflects the effect of contention rather than a confound. The estimand is therefore stated carefully as a conditional association under a named identifying assumption (5.3), not as an unconditional causal effect, and the boundary of the claim is carried explicitly into Section 5.5.

These three estimands map one-to-one onto the two clauses of the contribution's acceptance rule. The first estimand tests the wait-time-tail clause of H1. The second estimand tests the concentration clause. (The acceptance rule requires both clauses to pass; either failing refutes the contribution.) The third estimand does not gate acceptance; it localizes the carrying windows and supplies the mechanism-consistent evidence that Section 5.3 and Chapter 7 use to argue, with appropriately downgraded confidence, that contention rather than coincidence drives the concentration. Keeping the gating estimands (one and two) distinct from the localizing estimand (three) is what allows the design to earn the concentration result without overclaiming causation, and it is the single most important structural commitment of this chapter.

## 5.2 Estimators

Three estimators are used, each matched to one estimand and chosen because the structure of the corresponding data rules out the more familiar alternatives. The matching, not merely the list, is the argument here: a survival estimator is chosen for the wait estimand because the wait data are censored; a likelihood-based tail-fitting procedure is chosen for the tail estimand because least-squares fitting on log-log axes is known to be biased; and a fixed-effects regression is chosen for the driver estimand because the confounders the identification strategy must absorb are mission- and epoch-level.

### 5.2.1 Survival model of request-to-allocation time

The wait \(W_i\) is not a clean continuous outcome. A request that is still pending at the observation cutoff has a wait that is known only to exceed the elapsed time, and a request whose viewing window expires before allocation has a wait that is right-censored by the deadline rather than terminated by the event of interest. This is the defining structure of time-to-event data, and analyzing it with ordinary regression on observed waits would discard the censored requests or, worse, treat their truncated waits as completed ones, biasing the estimated distribution toward shorter waits precisely in the tail that the hypothesis is about [\[1\]](#ref-1), [\[2\]](#ref-2). That censored time-to-event data require survival methods rather than ordinary regression is foundational and uncontested in the methodological literature [\[3\]](#ref-3), [\[4\]](#ref-4); the survival function and the hazard function are defined so as to use the partial information in a censored observation (that the event had not yet occurred) rather than to drop it. One condition must be flagged: survival methods recover the wait distribution validly only if the censoring is non-informative in the standard sense, that the requests still pending or expired at the cutoff are not, conditional on covariates, systematically different in their latent wait from those allocated. This assumption is plausible for the administrative cutoff (a request pending only because the observation window ended) but is more delicate for deadline expiry, where the expired requests are exactly the deferred subclass the mechanism predicts. Section 5.5 treats this as a competing-risks concern and Section 5.6 addresses it with a competing-risks robustness specification.

Within the survival family, two estimators are used in sequence. The Kaplan-Meier estimator gives the nonparametric survival function \(S(t)\) of the wait, overall and stratified by load quartile, band, and mission phase [\[2\]](#ref-2), [\[5\]](#ref-5). It is chosen first because it imposes no functional form: the shape of \(S(t)\) in its tail is read directly, and a slowly declining tail is the first visual and quantitative signal of the heavy-tail estimand, before any parametric family is fit. The Cox proportional-hazards model then gives the covariate-adjusted hazard of allocation, \(h(t \mid X) = h_0(t)\exp(\beta'X)\), where the baseline hazard \(h_0(t)\) is left unspecified and the covariate vector enters multiplicatively [\[1\]](#ref-1), [\[6\]](#ref-6). The Cox model is chosen for the conditional wait structure because it is semiparametric: it estimates how geometry, band, and load shift the allocation hazard without committing to a parametric baseline that, if misspecified, would itself manufacture or mask a tail. Because concurrent load changes while a request waits, the load covariate is entered as time-varying, using the standard time-dependent-covariate extension of the Cox partial likelihood [\[3\]](#ref-3). The interpretive bridge to the wait estimand is the inverse-intuition complement: a covariate that lowers the allocation hazard lengthens the wait, so a negative coefficient on the allocation hazard for high concurrent load is the conditional-model expression of the same contention that the marginal tail-fit captures unconditionally. The two readings are designed to corroborate each other, and a divergence between them (a heavy unconditional tail with no corresponding load effect on the hazard) would itself be a finding worth reporting, because it would point the heavy tail toward a source other than load-driven deferral.

### 5.2.2 Heavy-tail distribution fitting

The tail estimand requires fitting candidate distributional families to the empirical wait and lost-downlink distributions and adjudicating among them. The estimator is the maximum-likelihood-plus-goodness-of-fit procedure of Clauset, Shalizi, and Newman, with likelihood-ratio comparison among non-nested candidates [\[4\]](#ref-4). The candidate set is fixed: the exponential serves as the light-tailed null benchmark, and the log-normal, the power-law (with exponent \(\alpha\)), and the generalized Pareto (scale \(\sigma\), shape \(\xi\)) for the upper tail serve as the heavier alternatives. The choice of this estimator over the once-common practice of regressing the log of the empirical complementary distribution on the log of the value is deliberate and is argued rather than assumed: log-log least-squares fitting produces biased exponent estimates and gives no principled goodness-of-fit test, which is exactly the failure mode that has populated the literature with spurious power laws [\[4\]](#ref-4). The Clauset-Shalizi-Newman procedure instead estimates the lower bound of the power-law regime and the exponent jointly by maximum likelihood, then assesses fit with a bootstrap Kolmogorov-Smirnov statistic, and then compares the fitted heavy-tailed candidate against the exponential and against the other heavy candidates by likelihood ratio, reporting which is preferred and with what significance. The procedure is preferred because it controls the false-positive rate that the hypothesis test is most exposed to, namely declaring a heavy tail where the data are consistent with a light one.

The upper tail is additionally estimated by a peaks-over-threshold generalized-Pareto fit, the standard extreme-value estimator for behavior above a high threshold. The estimand-relevant output is the shape parameter \(\xi\): a significantly positive \(\xi\) is the formal heavy-tail verdict, and its magnitude is the operational measure of how heavy. The generalized-Pareto fit is introduced as a complement to, not a substitute for, the full-distribution Clauset procedure because the two answer subtly different questions, the former about the conditional excess distribution above a threshold and the latter about the best global parametric description, and agreement between them is stronger evidence than either alone. The threshold-selection and full peaks-over-threshold protocol, including the mean-residual-life and parameter-stability diagnostics, belongs to the analysis plan and is specified in Chapter 6; the present chapter fixes only that the estimator is likelihood-based, that the exponential is the pre-registered null, and that the heavy verdict is operationalized through \(\xi\). A queueing-theoretic expectation makes the choice of estimator non-arbitrary: scheduling disciplines that defer a subclass of jobs are known to generate decreasing-hazard-rate tails in the waiting time [\[7\]](#ref-7), and the reinforcement-learning analysis of mixed heavy-tailed and light-tailed flows shows that a deferred subclass under a priority discipline produces precisely the heavy upper tail that a generalized-Pareto shape parameter is built to detect [\[8\]](#ref-8). The estimator is thus matched not only to the data type but to the specific tail behavior the mechanism predicts, which is why a tail-aware extreme-value estimator is preferred over a generic curve fit.

### 5.2.3 Pass-loss and lost-downlink regression

The driver estimand requires a conditional model of the binary pass-loss indicator \(L\) and of the continuous, skewed, non-negative lost-downlink magnitude \(D\). For \(L\), the estimator is a logistic regression of the log-odds of loss on the geometry covariates, band indicators, concurrent-load measures, and mission-phase indicators, with mission fixed effects \(\mu_m\) and epoch fixed effects \(\lambda_t\). The logistic form is chosen because the outcome is binary and the coefficients have a direct odds-ratio interpretation that the policy reading needs. For \(D\), the estimator is a generalized linear model with a link and variance function appropriate to skewed, non-negative, heavy-right support (a log-link gamma or, where the spike of zero-loss executed passes dominates, a two-part hurdle separating the loss-incidence margin from the loss-magnitude margin). The generalized-linear choice over ordinary least squares on \(D\) or on \(\log D\) is argued: \(D\) is bounded below at zero, is right-skewed by construction, and has a mass point at zero for executed passes, none of which a Gaussian linear model accommodates, and a naive \(\log D\) transform is undefined at the zero mass and distorts the very tail the study cares about. The fixed effects are not a nuisance device here; they are the identification instrument, and Section 5.3 makes the argument that \(\mu_m\) and \(\lambda_t\) absorb exactly the confounders that would otherwise contaminate the load and geometry coefficients.

The concentration estimand (estimand two) is, by contrast, not estimated by a regression at all. It is computed directly as the Gini coefficient \(G\) and top-decile share \(T_{10}\) of \(D_w\) across windows. This is stated here, in the estimator section, to make the point that the concentration result is a descriptive statistic of the realized record and inherits none of the identifying assumptions of the driver regression. The estimator for concentration is arithmetic on the window-aggregated loss; the only methodological care it requires is the small-sample bias correction for the Gini in the (possibly few) windows of a given stratum, which is a known and correctable issue and is carried into Chapter 6's protocol rather than into the identification argument here.

## 5.3 Identification strategy

Identification is treated as a first-class section because the three estimands differ sharply in what they require, and the credibility of the whole design depends on not letting the weakest identifying assumption travel to the strongest claim. The organizing distinction is between the two descriptive estimands, which require no exogeneity, and the one conditional estimand, which does.
### 5.3.1 The descriptive estimands need no exogeneity

The shape of the wait distribution and the concentration of lost downlink are properties of the realized log. The Kaplan-Meier survival curve, the fitted tail index \(\xi\), the Gini \(G\), and the top-decile share \(T_{10}\) are estimated from the complete record of requests, allocations, and executions. Their validity rests on the completeness and accuracy of that record, not on any claim that the covariates are exogenous to the requests. This is the design's deliberate firewall. If the concentration clause passes, the claim "lost downlink is concentrated on a minority of geometry-phase windows" is a statement about what the logs show, and it survives even if requested antenna time is thoroughly endogenous to expected contention, because the statement does not assert why the concentration occurs. A Gini coefficient and a tail index are functionals of the observed distribution; the only assumptions they carry are about measurement (Section 5.5's construct-validity discussion) and about sampling (the coverage requirement that the tail be observed often enough to fit, inherited from the proposal's multi-year coverage commitment and from the standard caution that short records undersample the tail). One limit on this firewall must be stated: descriptive does not mean assumption-free, it means free of the conditional-exogeneity assumption. The measurement assumptions remain and are treated where they belong.

### 5.3.2 The conditional estimand and its identifying assumption

The driver regression is where an identifying assumption enters. The identifying variation is the within-mission, within-epoch difference in pass-loss and wait as concurrent load and geometry vary across a mission's own requests in a given period. Mission fixed effects \(\mu_m\) absorb time-invariant mission characteristics: the instrument's nominal data rate, the mission's priority class, and its characteristic strategic-padding behavior, the systematic tendency of a given mission to inflate requested durations and submit early. Epoch fixed effects \(\lambda_t\) absorb network-wide shocks common to all missions in a period: an antenna in maintenance, a network-wide demand surge, a seasonal viewing pattern. The remaining variation used for identification is that a given mission, in a given period, faces different contention on different requests because of the geometry of its target and the coincidental load imposed by other missions. The identifying assumption is that this residual variation in load and geometry is, conditional on \(\mu_m\) and \(\lambda_t\), exogenous to that mission's own valuation of the specific pass.

This assumption is stated formally, with its mechanism, and then stress-tested. The driver-to-effect chain runs as follows: a given mission's request encounters higher concurrent load (driver) because other missions' independently scheduled targets happen to be well-placed in the same complex, band, and interval; the scheduling discipline, facing oversubscription, defers or shortens some request, and conditional on the mission's own fixed priority it is more likely to defer this mission's marginal request (mechanism); the request is lost or reduced (observable effect); lost downlink accrues to the window (operational consequence); and if such windows are a minority carrying a majority of loss, targeted remediation dominates broad remediation (strategic implication). The point of identification is to license the second link, that the higher loss probability reflects the contention rather than a confound. The fixed effects defend the link against the two most obvious confounds, mission-level padding and epoch-level shocks. What they do not by themselves defend against is a within-mission, within-epoch correlation between a mission's private valuation of a particular pass and the load it faces, if the mission times its high-value requests into windows it knows will be contested (for example, a critical encounter that is both scientifically precious and geometrically forced into a crowded window). This residual endogeneity is the design's central internal-validity threat and is named as such in Section 5.5.

### 5.3.3 The behavior-free robustness lever

To relieve the residual endogeneity that fixed effects cannot reach, the design introduces a source of variation in window compression that is set by celestial mechanics rather than by mission choice: the geometry-driven compression of a target's usable viewing window. The elevation profile of a target at a given complex, its declination, and conjunction or occultation conditions that shorten the usable window are determined by orbital and planetary geometry and are not selected by the mission. A specification that isolates the geometry-driven component of window compression, and uses it as a behavior-free source of contention variation, provides a robustness check on the load coefficient: if the loss-load association survives when contention is proxied by exogenous geometry compression rather than by behavior-laden requested-time load, the conditional claim is strengthened; if it collapses, the original association was likely contaminated by the timing-of-high-value-requests confound, and the confidence in the driver result is downgraded accordingly. This lever is presented honestly as a robustness instrument, not as a clean natural experiment: geometry compression is plausibly behavior-free, but it is not randomly assigned across missions (some missions have systematically harder geometry), so it relieves rather than eliminates the endogeneity, and the fixed effects are retained alongside it. The confidence posture for the driver estimand is therefore moderate at best at design stage, conditional on the geometry lever behaving as argued, and the chapter states plainly that the driver result is the more fragile of the three and that its policy reading is correspondingly qualified. The concentration result, by the 5.3.1 firewall, does not depend on any of this and retains higher design-stage confidence.

### 5.3.4 What identification does and does not buy

A positive result on the gating estimands would establish that the penalty is heavy-tailed and concentrated and would localize the carrying windows. It would not, by itself, establish causation of the concentration. The Forrester feedback account supplies the causal theory (looped, delayed feedback among locally optimizing missions piles contention onto shared windows), but the cross-sectional design tests that theory only indirectly, through the convex load-response signature estimated in Chapter 6 and through the driver regression's load coefficient under the geometry-lever robustness check. This boundary is stated plainly and is the limit of the claim: the design measures the shape and localizes the windows with high design-stage confidence; it argues the cause with moderate, mechanism-supported confidence and an explicit acknowledgment that a fully causal identification of the feedback mechanism would require post-intervention or quasi-experimental variation the present logs do not contain. The precautionary discipline adopted from the proposal's statistical frame applies here too: where the evidence supports only correlation, the design says so and downgrades confidence rather than dressing a correlation as a cause [\[9\]](#ref-9).

## 5.4 Model specifications

The specifications are written out so that the pre-registration in Section 5.8 has concrete objects to fix. Notation follows the definitions of Chapter 1 throughout.

### 5.4.1 Pass-loss probability

For request \(i\) of mission \(m\) in epoch \(t\), the index specification for the log-odds of pass-loss is

\[ \operatorname{logit}(\Pr(L_i = 1)) = \boldsymbol{\beta}_g' \mathbf{G}_i + \boldsymbol{\beta}_b' \mathbf{B}_i + \boldsymbol{\beta}_c' \mathbf{C}_i + \boldsymbol{\beta}_p' \mathbf{P}_i + \mu_m + \lambda_t + e_i \qquad\qquad (1) \]

where \(G_i\) is the vector of orbital-geometry covariates (target declination, viewing-window overlap among concurrently supported targets, elevation profile, conjunction or occultation compression of the usable window); \(B_i\) is the set of frequency-band indicators (S, X, Ka); \(C_i\) is the concurrent-mission-load vector (count and aggregate requested antenna-time of competing missions on the same complex, band, and interval); \(P_i\) is the mission-phase indicator set (launch, maneuver, encounter, entry-descent-landing, versus the cruise reference); \(\mu_m\) and \(\lambda_t\) are the mission and epoch fixed effects; and \(e_i\) is the idiosyncratic term. The coefficients of primary interest are \(\beta_g\), \(\beta_b\), and \(\beta_c\), the conditional associations the driver estimand targets. Standard errors are clustered to respect the dependence structure (by complex-interval, since requests competing in the same interval share the realized load), and the clustering choice is itself pre-registered because it materially affects the inference.

### 5.4.2 Lost-downlink magnitude

For the continuous penalty, the magnitude specification is a generalized linear model

\[ g(\mathbb{E}[D_i]) = \boldsymbol{\gamma}_g' \mathbf{G}_i + \boldsymbol{\gamma}_b' \mathbf{B}_i + \boldsymbol{\gamma}_c' \mathbf{C}_i + \boldsymbol{\gamma}_p' \mathbf{P}_i + \mu_m + \lambda_t \qquad\qquad (2) \]

with \(g\) a log link and a gamma (or, under overdispersion, an alternative skewed) variance function on the positive-loss observations, optionally combined with a logistic hurdle for the zero-loss (executed-as-requested) mass so that the incidence margin and the magnitude margin are modeled separately. The two-part structure is specified as the default because executed passes produce an exact zero in \(D\) that a single-part skewed GLM cannot represent, and the proposal's construct definition of \(D\) as the shortfall between requested and executed return makes the zero a true structural point, not a censored small value.

### 5.4.3 Allocation hazard

The Cox specification for the allocation hazard is

\[ h(t \mid \mathbf{X}_i) = h_0(t) \exp\!\bigl(\boldsymbol{\delta}_g' \mathbf{G}_i + \boldsymbol{\delta}_b' \mathbf{B}_i + \boldsymbol{\delta}_c' \mathbf{C}_i(t) + \boldsymbol{\delta}_p' \mathbf{P}_i\bigr) \qquad\qquad (3) \]

with the baseline hazard \(h_0(t)\) unspecified, the concurrent-load term \(C_i(t)\) entered as time-varying (its value updates as competing load changes while request \(i\) waits), and the proportional-hazards assumption itself treated as testable rather than assumed (Section 5.6 specifies the scaled-Schoenfeld-residual check and the stratified fallback). Mission and epoch effects enter by stratification of the baseline hazard where their number makes them better handled as strata than as covariates, a standard accommodation in the Cox framework [\[3\]](#ref-3), [\[6\]](#ref-6). The sign convention is fixed for interpretation: a negative \(\delta_c\) means high concurrent load lowers the allocation hazard and therefore lengthens the wait, the conditional-model expression of contention.

### 5.4.4 Tail and concentration objects

The tail specification fixes the candidate set {exponential (null), log-normal, power-law, generalized Pareto} and the peaks-over-threshold generalized-Pareto model for the conditional excess above a threshold \(u\), with parameters scale \(\sigma\) and shape \(\xi\); the heavy-tail verdict is \(\xi\) significantly greater than zero. The concentration objects are the Gini \(G\) of \(D_w\) and the top-decile share \(T_{10}\), computed on window-aggregated loss, with the small-sample Gini correction applied within sparse strata. These objects are specified here only to the level needed for pre-registration; their estimation protocol (threshold diagnostics, bootstrap goodness-of-fit, likelihood-ratio adjudication) is the subject of Chapter 6 and is cross-referenced rather than duplicated.
A pre-commitment governs both the tail fit and the concentration objects: the analysis stratifies each by scheduler-regime epoch before pooling. DSN scheduling policy is not stationary across the multi-year panel. The network has operated under different resource-allocation and priority regimes at different periods, reflecting changes in the mission manifest, in the allocation rule that adjudicates competing requests, and in the demand profile introduced by successive waves of spacecraft. Pooling observations across such regime boundaries and reporting a single tail shape or a single concentration coefficient would conflate a structural distributional property of the scheduling system with a period-specific artifact of whichever regime contributes more observations to the tail. The design therefore commits to the following procedure. Before the primary estimation, the panel is partitioned into scheduler-regime epochs using the available record of scheduling-policy changes and mission-manifest inflection points documented in the NTRS loading and forecasting reports [\[31\]](#ref-31) and in the operational history of the Service Preparation Subsystem. The tail fit (generalized-Pareto shape \(\xi\)) and the concentration objects (\(G\), \(T_{10}\)) are estimated within each epoch separately, and the epoch-specific estimates are compared before any pooled estimate is reported. If the epoch-specific estimates are materially consistent, the pooled estimate is defensible and is reported as the primary result, with the within-epoch consistency noted as evidence of robustness. If the epoch-specific estimates diverge, the pooled result is suppressed as uninterpretable, and the primary reported result is the epoch-stratified set; the contribution's claim is then bounded to the regime or regimes in which the heavy-tail and concentration signature is observed, with the divergent epochs reported as scope conditions rather than counter-evidence. In the limiting case where one regime dominates the tail observations so completely that the others cannot be fitted reliably, the design pre-commits to restricting the primary analysis panel to that regime and reporting the restriction explicitly, so that the sample boundary matches the inferential claim. This stratification commitment is pre-registered alongside the primary decision rules of Section 5.8, and no post-hoc pooling across regime epochs is permitted after the estimates are inspected.

## 5.5 Threats to validity

The threats are enumerated across the four standard categories, each with a named, design-internal mitigation. Here the argument's discipline applies to the design itself: the problem is real and material (established in Chapters 1 and 2), the design addresses the mechanism (5.2, 5.3), and the residual risk is acceptable only to the extent each threat below is bounded.

### 5.5.1 Internal validity

The principal internal-validity threat is the endogeneity of requested time to expected contention, identified in 5.3.2: missions that anticipate a hard window pad their requested durations and escalate priority, so load and loss are jointly determined by an unobserved expectation, and within-mission timing of high-value requests into forced-crowded windows can survive the fixed effects. The mitigation is layered. Mission fixed effects \(\mu_m\) absorb the systematic component of padding and priority behavior; epoch fixed effects \(\lambda_t\) absorb network-wide shocks; and the geometry-driven window-compression lever (5.3.3) provides a behavior-free contention proxy as a robustness check on the load coefficient. The residual, the within-mission, within-epoch correlation between private pass valuation and geometry-forced crowding, is acknowledged as not fully eliminable from cross-sectional logs, and the driver-estimand confidence is downgraded to moderate accordingly. The concentration estimand is insulated from this threat by the 5.3.1 firewall and retains its higher confidence.

A second internal-validity concern is informative censoring in the survival model: deadline-expired requests are precisely the deferred subclass the mechanism predicts, so treating their censoring as non-informative could bias the wait distribution. The mitigation is the competing-risks treatment specified in 5.6, which models allocation and expiry as competing events rather than treating expiry as ordinary censoring [\[10\]](#ref-10); the naive Kaplan-Meier that treats a competing event as censored is known to be biased, and the cause-specific and cumulative-incidence formulation is the established correction [\[10\]](#ref-10).

### 5.5.2 External validity

The penalty's shape may be specific to the studied epoch's mission mix. The crewed-exploration era is projected to shift the mix toward high-rate, time-critical traffic and to raise loading substantially [\[11\]](#ref-11), [\[12\]](#ref-12), which the design cannot observe in advance. The mitigation is twofold and is inherited from the proposal's stance: claims are explicitly conditioned on the studied mix, and the externally valid object reported is the load-response curve (the relationship between expected lost downlink and concurrent load), not a single satisfaction rate, because the curve predicts how the penalty would scale as load rises and is therefore the quantity an exploration-era planner needs. A convex curve implies a worse-than-linear exploration-era penalty, which is itself the planning-relevant external inference. Extrapolation beyond the observed load range is flagged as extrapolation and is not asserted as established.

### 5.5.3 Construct validity

Lost downlink is a proxy for lost science return, and the proxy is imperfect: not all bits carry equal scientific value, and a navigation-critical tracking pass lost in a specific mission phase has a value that a data-volume measure does not capture. The mitigation is to report the penalty in two constructs, the data-volume \(D\) and, where mission records permit, a criticality-weighted \(D\) that up-weights mission-declared critical-event windows, with the gap between the two constructs reported rather than hidden. The proposal flags the criticality weights as the least-sourced input; the design therefore treats the criticality-weighted construct as a robustness construct whose feasibility is partial, and does not let the headline claim depend on weights that may be incompletely available. A second construct concern is that \(D\) depends on assumed nominal data rates that vary with link conditions, introducing measurement error in the dependent variable; the mitigation is a sensitivity analysis over the data-rate assumption (5.6) and a plain statement that this measurement error inflates the variance of the magnitude estimates.

### 5.5.4 Statistical-conclusion validity

Heavy-tail fitting is prone to false positives when samples are small or thresholds are chosen post hoc, and concentration measures are prone to small-sample bias. The mitigations are the Clauset-Shalizi-Newman goodness-of-fit step, the pre-registered threshold-selection diagnostics, and the likelihood-ratio comparison against the exponential, all with the decision rule fixed before estimation [\[4\]](#ref-4), so that a heavy-tail verdict is earned against a pre-committed null rather than discovered by threshold-shopping. For concentration, the small-sample Gini bias is corrected within sparse strata, a known and signable bias whose correction is applied as a matter of course. Multiple-comparison exposure (the design fits tails and runs regressions across several strata) is controlled by pre-registering the primary tests and labeling all stratum-level results as secondary and exploratory, so that the gating decision rests on the pre-registered primary tests alone. The proposal's both-outcomes-are-useful stance is the statistical-conclusion-validity backstop: the null is a live, reportable outcome, and the design is built so that retaining H0 (light tail, near-uniform concentration, linear load-response) is a clean and publishable result, not a failure to be avoided.

## 5.6 Robustness battery

The robustness checks are specified in advance and grouped by the threat each addresses, so that the pre-registration can commit to running them regardless of whether the primary results are favorable.

First, **competing-risks survival**: re-estimate the wait analysis treating allocation and deadline-expiry as competing events, reporting cause-specific hazards and cumulative-incidence functions, to test whether the informative-censoring concern materially changes the wait-distribution verdict [\[10\]](#ref-10). Second, **proportional-hazards diagnostics**: test the Cox proportional-hazards assumption with scaled Schoenfeld residuals and, where it fails, refit with stratification or time-interaction terms rather than reporting a violated model [\[3\]](#ref-3). Third, **the geometry-lever robustness specification**: re-estimate the driver regression with contention proxied by exogenous geometry-driven window compression in place of behavior-laden requested-time load, reporting whether the load association survives (5.3.3). Fourth, **leave-one-mission-out**: re-estimate the concentration and driver results dropping each mission in turn, to confirm that the concentration is a structural property and not an artifact of a few atypical missions. Fifth, **threshold sensitivity** for the tail fit: report the fitted shape \(\xi\) across a range of thresholds around the diagnostic-selected \(u\), to confirm parameter stability rather than a single fragile threshold (the full threshold protocol is Chapter 6). Sixth, **science-usefulness-threshold sensitivity**: vary the threshold that classifies a reduced pass as lost, since that threshold is a modeling choice flagged in the proposal's data limitations, and report the concentration and driver results across the range. Seventh, **data-rate sensitivity**: vary the assumed nominal data rate that maps a lost pass to lost-downlink magnitude, propagating the measurement error into the magnitude estimates. Eighth, **criticality-weighted construct**: where feasible, re-run the concentration result on the criticality-weighted \(D\) to separate high-value-by-selection from high-loss-by-contention. Ninth, **scheduler-regime epoch stratification**: as specified in 5.4.4, re-estimate the tail shape \(\xi\) and the concentration objects \(G\) and \(T_{10}\) within each identified scheduler-regime epoch separately and compare the within-epoch estimates to the pooled result; if the epoch-specific estimates are materially inconsistent, the pooled result is suppressed and the primary inference is restricted to the epoch or epochs that support it, with the restriction reported as a scope condition on the contribution. This check is not optional: DSN scheduling policy has changed across the multi-year panel, and a pooled tail or concentration estimate that masks regime-level heterogeneity would overstate the generality of the finding [\[31\]](#ref-31). Each check maps to a threat in 5.5, and the design commits to reporting all nine regardless of outcome, which is the operational meaning of the pre-registration.

## 5.7 Power and minimum-detectable-effect analysis

A design-stage power analysis is required because the gating tests are tests of distributional shape, and shape tests have power properties that differ from mean-comparison power and that the multi-year coverage requirement is meant to satisfy. The analysis here illustrates the form the power calculation takes; the numbers are **illustrative placeholders, not computed estimates**, because no log has been analyzed and the realized sample sizes are unknown at design stage.

For the **wait-time tail clause**, the relevant power is the probability that the likelihood-ratio test prefers a heavy-tailed candidate over the exponential, and that the generalized-Pareto shape parameter \(\xi\) is detected as significantly positive, given a true \(\xi\) of a particular magnitude. The minimum detectable effect is therefore framed as the smallest true \(\xi\) that the design can reliably distinguish from zero at the pre-registered significance and a target power (illustratively, eighty percent). Heavy-tail detection power is governed chiefly by the number of observations in the tail above the threshold, not by the total sample, which is the analytic reason the proposal commits to multi-year coverage: the tail must be observed often enough to fit, and short records undersample exactly the region the test depends on. The illustrative reasoning is that detecting a moderately heavy tail (illustrative true \(\xi\) in the range the proposal labels for a positive result, on the order of 0.3 to 0.5) at eighty percent power requires a tail sample of order hundreds of above-threshold observations; the design's coverage target is set so that several cycles of the recurring high-contention windows supply that tail sample. If the realized tail sample falls short, the design pre-commits to reporting the achieved power and widening the uncertainty interval on \(\xi\) rather than forcing a verdict, which preserves statistical-conclusion validity.

For the **concentration clause**, the minimum detectable effect is the smallest departure of the top-decile share \(T_{10}\) from the 0.10 uniformity benchmark (and the corresponding Gini departure from zero) that the design can distinguish from sampling variation at the pre-registered level. Because concentration is a descriptive functional, its sampling distribution is obtained by bootstrap over windows, and the power question is whether the number of geometry-phase windows is large enough that a true \(T_{10}\) materially above 0.10 (illustratively, the 0.5 to 0.67 the proposal labels for a positive result) is reliably separated from the benchmark. The illustrative reasoning is that with a window count in the hundreds, a true \(T_{10}\) near one-half is separated from 0.10 with high power, while a true \(T_{10}\) near 0.15 would require many more windows to detect, so the design's minimum detectable concentration is modest and the risk is one of failing to detect weak concentration, not of spuriously detecting strong concentration. For the **driver regression**, the minimum detectable effect is the smallest odds-ratio on concurrent load (and on geometry compression) that the within-mission, within-epoch variation supports at target power, which depends on the number of requests per mission-epoch cell and on the residual variation in load after the fixed effects absorb the between-mission and between-epoch components; the design pre-commits to reporting the achieved minimum detectable odds-ratio so that a null load coefficient is interpretable (a true null versus an underpowered cell). All three minimum-detectable-effect targets are fixed in the pre-registration so that the post-estimation report can state whether the design was adequately powered for each clause, and the multi-year coverage requirement is justified precisely as the lever that buys tail-sample and window-count adequacy.

## 5.8 Pre-registration commitment

The design commits to pre-registration before any estimation is run, and the pre-registration document is the appendix the proposal names. The commitment is substantive, not ceremonial: it fixes, in writing and before the logs are touched, the three estimands (5.1), the three estimators and their specifications (5.2, 5.4), the identifying assumption and the geometry-lever robustness check (5.3), the candidate distribution set and the exponential null for the tail test (5.4.4), the threshold-selection diagnostics (deferred in protocol to Chapter 6 but named in the pre-registration), the concentration metrics \(G\) and \(T_{10}\), the eight-item robustness battery (5.6), the clustering and standard-error choices (5.4.1), and, above all, the decision rules. The decision rules are carried verbatim from the prospectus: the wait-time-tail clause of H1 is accepted only if the likelihood-ratio test prefers a heavy-tailed model over the exponential at the pre-set significance and the generalized-Pareto shape \(\xi\) is significantly positive; the concentration clause is accepted only if \(T_{10}\) is materially above the ten-percent benchmark (a pre-registered threshold, illustratively \(T_{10}\) at or above 0.40) with a correspondingly elevated \(G\); and the contribution as a whole is accepted only if both clauses pass, with either clause failing refuting it. Pre-registering these rules is the mechanism that converts the heavy-tail and concentration tests from exploratory data description into confirmatory tests, and it is the specific control on the statistical-conclusion-validity threat of threshold-shopping (5.5.4). The pre-registration also fixes the boundary of the causal claim (5.3.4), so that the driver result cannot be silently upgraded from association to cause after the fact. The both-outcomes-are-useful commitment is registered explicitly: retaining H0 is pre-declared a reportable result, which removes the incentive to mine the data for a positive verdict and is itself a precautionary safeguard consistent with the design's statistical frame [\[9\]](#ref-9).

## 5.9 Computational and software plan

The computational plan names the tooling so that the analysis is reproducible and so that the estimators of 5.2 are implemented in their established, tested forms rather than re-coded. Survival estimation (Kaplan-Meier, Cox proportional hazards with time-varying covariates, competing-risks cause-specific and cumulative-incidence models) is implemented in the standard survival-analysis stacks whose conventions the methodological references document [\[3\]](#ref-3), [\[13\]](#ref-13), [\[14\]](#ref-14); the time-varying-covariate and stratified-baseline accommodations specified in 5.4.3 are standard features of those stacks. Heavy-tail fitting follows the Clauset-Shalizi-Newman procedure as implemented in the established packages: the Python `powerlaw` package and the R `poweRlaw` package both implement the maximum-likelihood fit, the bootstrap goodness-of-fit, and the likelihood-ratio model comparison, and either is acceptable provided the pre-registered candidate set and null are used [\[15\]](#ref-15), [\[16\]](#ref-16). The peaks-over-threshold generalized-Pareto fit and its threshold diagnostics are implemented in the standard extreme-value-theory libraries (the protocol detail belongs to Chapter 6). Concentration metrics (\(G\), \(T_{10}\), the small-sample Gini correction) are computed with established inequality-measurement code whose definitions the references fix [\[17\]](#ref-17), so that the Gini is the textbook functional and not an ad hoc variant. The logistic and generalized-linear regressions with high-dimensional fixed effects are implemented in fixed-effects-aware regression libraries that absorb \(\mu_m\) and \(\lambda_t\) efficiently and produce the clustered standard errors specified in 5.4.1.

The plan commits to reproducibility discipline appropriate to a design that will eventually touch access-controlled logs. The data-assembly pipeline that joins the DSN scheduling and tracking logs to mission downlink-requirement records and derived geometry covariates (the panel-construction step that Chapter 6 details) is to be scripted and version-controlled so that the request-level panel is regenerable from the raw inputs. Where direct log access is constrained for some intervals, the proposal's fallback of reconstructing time-to-event panels from published Kaplan-Meier-style summaries is available as a documented secondary procedure, with the reconstruction method and its accuracy caveats recorded [\[18\]](#ref-18), and any interval so reconstructed is flagged in the analysis so that the coarsening of the load covariate noted in the proposal's limitations is visible in the results rather than buried. Random seeds for the bootstrap goodness-of-fit and the bootstrap concentration intervals are fixed and recorded, the package versions are pinned, and the pre-registration and the codebook are versioned alongside the code so that the design as specified here and the design as executed can be compared line by line. This reproducibility commitment is the operational guarantee that the residual risk stays acceptable: a reader can in principle re-run the design and confirm that the verdict on each clause followed the pre-registered rule from the realized log, which is the property that makes a design-stage plan auditable rather than merely asserted.

## 5.10 Summary of the design
Three estimands are matched to three estimators under an identification strategy that firewalls the descriptive estimands from the conditional one. The wait-time shape is recovered by survival analysis (Kaplan-Meier plus Cox with time-varying load) and adjudicated against an exponential null by likelihood-based heavy-tail fitting, with the generalized-Pareto shape \(\xi\) as the heavy-tail verdict. The concentration of lost downlink is computed directly as \(G\) and \(T_{10}\) on window-aggregated loss; this descriptive result requires no exogeneity assumption, which is why it carries the higher design-stage confidence and gates the contribution alongside the tail clause. The conditional drivers are estimated by fixed-effects logistic and skewed-GLM regression whose load and geometry coefficients are identified by within-mission, within-epoch variation, defended by \(\mu_m\) and \(\lambda_t\) and relieved, not eliminated, by the behavior-free geometry-compression lever, so that the driver result is reported at moderate confidence with its endogeneity boundary explicit. Every threat across internal, external, construct, and statistical-conclusion validity is named and paired with a design-internal mitigation; the robustness battery is pre-committed; the power analysis fixes a minimum detectable effect for each clause and justifies the multi-year coverage as the lever that buys tail-sample and window-count adequacy; and the decision rules and estimands are pre-registered before any log is touched. No result in this chapter is executed: every illustrative magnitude is labeled as such, and the null remains a live, pre-declared, reportable outcome. The design earns the strong concentration claim where the data support it, tests the tail claim against a pre-committed null, and argues the causal mechanism only as far as cross-sectional logs and the geometry lever license, which is the honest boundary the contribution is meant to respect.


# Chapter 6: Analysis Plan and Expected Results

## 6.0 The chapter's answer

One question must be answered before any number can be reported. Given the data described in Chapter 4 and the estimators specified in Chapter 5, exactly what computations will be run, in what order, against what fixed decision rule, and what shape would the results take if the structural mechanism of Chapter 2 is correct? The answer is that the test of the dissertation's single contribution reduces to a small, pre-registered sequence of estimations whose acceptance criteria are fixed before any DSN log is touched, so that the conclusion is determined by the data and the rule rather than by the analyst's discretion after seeing the data. The plan proceeds in five steps: assemble the request-level panel, estimate the wait-time distribution and its tail, estimate the concentration of lost downlink across windows, estimate the conditional drivers of pass-loss, and estimate the load-response curve. Each step has a stated estimand from Chapter 5, a stated estimator, a stated output object, and, where the contribution depends on it, a stated threshold that converts the output into an accept-or-reject verdict on a clause of the hypothesis. The apparatus is built so that the null, that the science-throughput penalty is uniform and light-tailed, is a live and reportable outcome rather than a foil the design quietly rules out.

A note on epistemic posture follows, restated here because this chapter is where the temptation to overclaim is strongest. No estimation has been run. The Kaplan-Meier curve has not been computed; the generalized-Pareto shape parameter has not been estimated; the Gini coefficient and the top-decile loss share do not yet exist as numbers. Every magnitude that appears in Section 6.5 is an illustrative placeholder chosen to show the *form* a positive result would take, and each such magnitude is labeled illustrative at the point of use. No figure from this chapter should be carried forward as an estimate. The confidence attached to the *mechanism* that predicts a heavy tail and concentration is moderate-to-high, because three independent theoretical traditions converge on it (Chapter 2); the confidence attached to whether the real logs realize that prediction is, by construction, undetermined until the plan is executed. Pre-registering the plan in this much detail fixes the decision rule while the empirical answer is still unknown, which is the condition under which a test is informative rather than merely confirmatory.

## 6.1 The problem this chapter addresses

The same current-state, desired-state, gap, consequence structure used throughout the dissertation applies here, narrowed to the act of estimation itself.

The current state of practice, established in Chapters 3 and 5, is that the DSN scheduling literature reports the residual cost of contention either as an aggregate satisfaction rate or as the objective value of an optimizer, and that the survival, heavy-tail, and concentration estimators needed to characterize the distributional shape of the penalty exist as mature methods in their home disciplines but have never been assembled and aimed at DSN scheduling logs [\[10\]](#ref-10), [\[33\]](#ref-33), [\[4\]](#ref-4), [\[76\]](#ref-76). The desired state is a fully specified estimation pipeline that takes the request-level panel of Chapter 4 as input and returns, as output, a verdict on each clause of the hypothesis together with the quantitative objects, a fitted tail, a concentration curve, a load-response curve, that a planner could act on.

The gap between the two is not a gap of available methods but a gap of *specification and pre-commitment*. Heavy-tail fitting is vulnerable to false positives when the threshold above which the tail is fitted is chosen after inspecting the data, when the candidate distributions are compared informally, or when goodness-of-fit is asserted rather than tested [\[4\]](#ref-4), [\[6\]](#ref-6). Concentration measures such as the Gini coefficient are biased in small samples, and the bias has repeatedly been mistaken for a substantive trend [\[77\]](#ref-77). A plan that did not fix the threshold-selection procedure, the model-comparison test, and the small-sample correction in advance could manufacture support for the alternative from noise. The consequence of leaving the plan unspecified is not merely untidiness; the eventual finding becomes uninterpretable, because the reader cannot distinguish a real heavy tail from an artifact of analyst freedom. Writing the pipeline down completely and binding it to fixed decision rules, so that the analysis can only return the answer the data dictate, is the work this chapter does.

## 6.2 The five pre-registered estimation steps

The estimation proceeds in five steps, presented in execution order. For each step the account states what the step does, the basis on which it rests, and what licenses moving from the step's output to the inference it supports.

### 6.2.1 Step one: assemble the request-level panel

The analysis panel is assembled from the three named data sources of Chapter 4. The DSN scheduling and tracking logs supply one row per tracking-pass request, the primary unit of analysis defined in Chapter 1: one requested activity, one mission, one antenna class, one viewing window. To each request row the step joins the mission downlink-requirement records, which convert a lost or reduced pass into a lost-downlink magnitude, and the derived orbital-geometry covariates (declination, viewing-window overlap, elevation profile, conjunction or occultation compression). The output is a single table in which each request *i* carries its wait time \(W_i\), its censoring indicator \(c_i\), its pass-loss indicator \(L_i\), its lost-downlink magnitude (defined at the window level as \(D_w\) after aggregation), and the covariate vector \(X\) of geometry, band, concurrent-mission load, and mission-phase indicator.

The reason for treating this assembly as a defined construct rather than a raw extract is laid out in Chapter 4: requested time is a hedged quantity reflecting strategic padding and early submission, not a clean demand signal, and the science-usefulness threshold that distinguishes a reduced-but-useful pass from a lost pass is a modeling choice. Proceeding despite these qualifications is justified because each is carried forward as a sensitivity parameter rather than buried, and where direct log access is constrained for some intervals, the panel is supplemented by reconstructing time-to-event information from the aggregated loading reports using the published method for recovering individual-level survival data from summary curves [\[88\]](#ref-88). One limit on this step is explicit: the reconstruction method recovers an approximation, not the original micro-data, so intervals filled this way are flagged and entered into a robustness check rather than pooled silently with directly observed intervals. The objection the step must survive is that the assembled panel is unrepresentative because access constraints bias which intervals are observed; the mitigation is the multi-year coverage requirement of Chapter 4, which is designed so that several cycles of the recurring high-contention windows are observed directly rather than reconstructed.

### 6.2.2 Step two: estimate the wait-time distribution and its tail

The first clause of the contribution is a claim about the upper tail of the request-to-allocation wait-time distribution, so this step goes directly there. The step has two parts. The nonparametric part computes the Kaplan-Meier survival function \(S(t)\) of the wait, overall and stratified by load quartile, by band, and by mission phase [\[2\]](#ref-2), [\[65\]](#ref-65). Stratification is not decoration: it is the first visual diagnostic of whether the tail behavior differs across the strata that the mechanism predicts should carry the load, and a divergence of the stratified survival curves at long waits is the qualitative signature the formal tail test then quantifies. Because some requests are right-censored (pending at the observation cutoff) and some experience a competing terminal event (the viewing window expires before allocation, which is loss rather than allocation), the survival estimation respects the competing-risks structure: the naive Kaplan-Meier estimator that treats the competing event as ordinary censoring is biased for the cause-specific quantity of interest, so the cause-specific hazard and cumulative-incidence formulation is used where allocation and expiry compete [\[64\]](#ref-64).

The parametric part fits candidate distributions to the wait and to its tail. The exponential is the light-tailed null benchmark, the distribution the wait would follow if the schedule behaved like a memoryless server with no priority structure. Against it are fit the log-normal, the power-law, and, for the upper tail above a high threshold, the generalized Pareto distribution. The basis for this candidate set is theoretical: Chapter 2 names three concurrent queueing routes to a heavy wait tail (hard viewing-window deadlines producing deadline-driven abandonment, bursty clustered arrivals, and skewed service requirements), and each route is associated in the queueing literature with a non-exponential wait tail, whether through the priority-discipline mechanism that freezes low-priority tasks [\[83\]](#ref-83), [\[82\]](#ref-82), through self-similar and heavy-tailed arrival structure [\[51\]](#ref-51), [\[52\]](#ref-52), or through the Markov-modulated and phase-type tail results that bound how far a modulated or multi-class queue departs from the averaged exponential [\[80\]](#ref-80), [\[46\]](#ref-46). Fitting all candidates rather than assuming the heavy one follows Taleb's methodological instruction adopted in Chapter 2: do not assume the tail, test for it, and prefer the heavier model only if the data reject the lighter one (the precautionary inversion of the burden of proof). The detailed fitting protocol, including the threshold selection and the model-comparison test, is specified in Section 6.3.

### 6.2.3 Step three: estimate the concentration of lost downlink

How lost downlink distributes across the secondary unit of analysis, the geometry-phase window defined in Chapter 1 as a discretized cell of orbital-geometry condition by mission phase by complex by band, is what this step measures. The step aggregates the request-level lost-downlink magnitudes into the window-level quantity \(D_w\), then summarizes the distribution of \(D_w\) across windows with two complementary concentration statistics and one curve. The first statistic is the Gini coefficient \(G\) of \(D_w\) across windows, the standard summary of how unequally a resource (here, loss) is distributed over a population (here, windows) [\[76\]](#ref-76). The second is \(T_{10}\), the share of total lost downlink carried by the top decile of windows ranked by \(D_w\); under uniformity \(T_{10}\) is close to ten percent, and a value materially above ten percent is the direct operationalization of concentration. The curve is the plot of cumulative lost downlink against window rank, the Lorenz-type object whose curvature *is* concentration made visible.

The basis for importing inequality measurement into a scheduling study is that the formal question is identical: the Gini coefficient and the concentration index were built to answer exactly "does a small fraction of the population carry a large fraction of the quantity," and they come with an established inferential apparatus including standard errors and group comparison [\[78\]](#ref-78), [\[79\]](#ref-79). Relying on them here is sound, though the principal threat the step must manage is the small-sample bias of the Gini coefficient: in a population of few windows the coefficient is biased downward, and the bias has historically been misread as a real difference in concentration [\[77\]](#ref-77). The step therefore applies the small-sample correction and reports both the corrected and uncorrected coefficients, and it leans more heavily on \(T_{10}\), which has a more transparent interpretation, when the number of populated windows is small. Concentration is a *descriptive* property of the realized log: unlike the driver regression of Step four, the concentration estimate does not require any conditional-exogeneity assumption, because it makes no causal claim. It stands or falls on the completeness of the log, not on an identification argument, which is why Chapter 5 places it outside the identification strategy and inside the descriptive layer.

Before the pooled \(G\) and \(T_{10}\) are reported as primary results, this step executes the scheduler-regime epoch stratification committed to in Section 5.4.4 and listed as the ninth robustness check in Section 5.6. The panel is partitioned by scheduler-regime epoch, \(G\) and \(T_{10}\) are computed within each epoch, and the within-epoch estimates are presented alongside the pooled figures. A pooled concentration estimate is reported as the primary result only when the epoch-specific estimates are materially consistent; where they diverge, the epoch-stratified results are the primary output and the pooled figure is reported as a summary that masks the heterogeneity. This sequencing is fixed before estimation: the epoch comparison runs first, and the decision about whether to lead with the pooled or the stratified result follows from that comparison rather than from which figure is more favorable to the alternative hypothesis.

### 6.2.4 Step four: estimate the conditional drivers of pass-loss

Holding mission and epoch fixed, this step estimates the conditional association between pass-loss and its hypothesized drivers. Three models share the covariate vector \(X\). The Cox proportional-hazards model estimates the allocation hazard \(h(t \mid X) = h_0(t)\exp(\beta'X)\), with concurrent load entered as a time-varying covariate because the load a request faces changes while it waits [\[1\]](#ref-1), [\[3\]](#ref-3), [\[66\]](#ref-66). The logistic model regresses the binary pass-loss indicator \(L_i\) on geometry, band, concurrent load, and mission-phase indicators, with mission fixed effects \(\mu_m\) and epoch fixed effects \(\lambda_t\). The skewed generalized-linear model regresses the continuous, non-negative, right-skewed lost-downlink magnitude on the same covariates with an appropriate link and variance function.

The basis for the fixed-effects specification is the identification argument of Chapter 5: mission fixed effects absorb the time-invariant mission characteristics (instrument data rate, priority class, padding behavior) that would otherwise confound the load and geometry coefficients, and epoch fixed effects absorb network-wide shocks common to all missions in a period. The coefficients can be read as drivers rather than mere associations because of the within-mission, within-epoch variation that survives the fixed effects: a given mission, in a given period, faces different contention on different requests because of the geometry of its target and the coincidental load from others, variation that is plausibly exogenous to that mission's own valuation of the specific pass. One boundary is firm: this is a conditional association under a stated identifying assumption, not a structural treatment effect, and the objection that requested time is endogenous to expected contention (missions that anticipate a hard window pad and escalate) is addressed by the geometry-driven window-compression robustness check of Chapter 5, in which the celestial-mechanics-determined viewing window, which no mission chooses, supplies behavior-free variation. The hazard direction must be read with care and is stated once: covariates that *lower* the allocation hazard *lengthen* the wait, so a negative load coefficient in the Cox model is the expected sign for a driver of contention.

### 6.2.5 Step five: estimate the load-response curve
The contribution's risk reading, drawn from Taleb in Chapter 2, turns on the *curvature* of the response of expected lost downlink to concurrent-mission load rather than on any single point estimate, which is why this step exists. The step plots expected lost downlink (and, in a parallel version, expected wait) against concurrent-mission load, and tests whether the response is convex, that is, whether lost downlink rises faster than linearly as load increases. Convexity is estimated two ways: nonparametrically, by fitting a flexible smoother to the loss-versus-load relationship and inspecting the second difference, and parametrically, by including a quadratic or spline term in load in the loss model of Step four and testing its coefficient.

The basis for elevating curvature to a primary estimand is the fragility framework. A convex response of a system's loss to the dose of a stressor is the formal signature of fragility, and the Jensen-gap characterization makes the second-order response, not the forecast of the stressor, the object to estimate [\[28\]](#ref-28), [\[29\]](#ref-29). What connects this to the dissertation's claim is that a convex load-response is a third, independent line of evidence for concentration: if loss accelerates with load, then the high-load windows carry disproportionate loss by construction, which is concentration viewed through the load covariate rather than through the window ranking of Step three. The load-response curve is also the externally valid object the design produces, in the sense that it predicts how the penalty would scale into the higher-load crewed-exploration era that the data do not yet contain [\[17\]](#ref-17), [\[31\]](#ref-31); a single satisfaction rate cannot do this, and the curve is reported precisely so that extrapolation is explicit rather than hidden. The objection that an apparent convexity could be an artifact of a few extreme high-load points is handled by the same robustness logic as the tail fit, reported with and without the most extreme load decile.

## 6.3 The heavy-tail fitting protocol

The first clause of the contribution rests entirely on whether the wait-time and lost-downlink tails are heavier than exponential, so the fitting protocol is specified in full and fixed before estimation, in keeping with the chapter's pre-registration logic. The protocol has four components: candidate fitting, threshold selection, model comparison, and goodness-of-fit.

Candidate fitting follows the maximum-likelihood procedure of the Clauset-Shalizi-Newman framework, which fits each candidate distribution by maximum likelihood rather than by the discredited practice of linear regression on log-log axes, the latter known to produce biased and overconfident exponent estimates [\[4\]](#ref-4). The framework is implemented in the `powerlaw` Python package and the `poweRlaw` R package, either of which supplies the maximum-likelihood fit, the bootstrap goodness-of-fit, and the likelihood-ratio model comparison used below [\[5\]](#ref-5), [\[6\]](#ref-6). For the power-law candidate the relevant parameter is the exponent \(\alpha\); for the generalized-Pareto candidate the relevant parameters are the scale \(\sigma\) and the shape \(\xi\), and `xi > 0` is the formal heavy-tail signature on which the wait-time clause's decision rule depends.

Threshold selection is the single most consequential and most abused choice in tail fitting, and the protocol removes analyst discretion from it. The lower threshold above which the power-law or generalized-Pareto tail is fitted is chosen by a fixed, data-driven criterion rather than by eye. For the power-law fit, the Clauset-Shalizi-Newman procedure selects the threshold that minimizes the Kolmogorov-Smirnov distance between the fitted model and the empirical tail, which is a defined function of the data and not a judgment [\[4\]](#ref-4). For the generalized-Pareto peaks-over-threshold fit, the threshold is selected by the standard extreme-value diagnostics: the mean-residual-life plot, which should be approximately linear above a valid threshold, and the parameter-stability plot, which should show the shape estimate stabilizing above a valid threshold [\[54\]](#ref-54), [\[58\]](#ref-58). Because threshold choice carries irreducible uncertainty even under these diagnostics, the protocol additionally reports a Bayesian treatment that models the threshold as an unknown parameter and propagates its uncertainty into the tail estimate rather than conditioning on a single chosen value [\[57\]](#ref-57). The reason for this triangulation is that a heavy-tail conclusion robust to all three threshold treatments is far harder to dismiss as an artifact than one that depends on a single hand-chosen cut.

Model comparison among the non-nested candidates uses the likelihood-ratio test of Vuong type that the Clauset framework supplies: the exponential null is compared against each heavier candidate, and the test returns both a sign (which model is favored) and a significance (whether the preference is statistically distinguishable from a tie) [\[4\]](#ref-4), [\[5\]](#ref-5). The decision rule of Section 6.4 is written in terms of this test. Where the degree distribution or loss distribution is large-scale and the simple power law fits the body poorly, the protocol admits the modified-Lomax and phase-type-scale-mixture alternatives as additional heavy-tailed candidates that fit body and tail jointly, so that a poor body fit is not mistaken for an absence of a heavy tail [\[87\]](#ref-87), [\[59\]](#ref-59). For conditional tail estimation, where the question is how the tail depends on covariates rather than its marginal shape, the protocol uses gradient-boosting extreme quantile regression on the peaks-over-threshold formulation, which estimates a covariate-dependent generalized-Pareto tail and is better suited to high-dimensional predictors than classical quantile regression [\[96\]](#ref-96).

Goodness-of-fit is tested, not asserted. The bootstrap goodness-of-fit step of the Clauset framework simulates many synthetic datasets from the fitted model, refits each, and computes the fraction whose Kolmogorov-Smirnov distance exceeds that of the real fit; a small fraction means the model is rejected as a plausible generator of the data [\[4\]](#ref-4), [\[6\]](#ref-6). The caution carried throughout is statistical-conclusion validity: heavy-tail fitting produces false positives when samples are small or thresholds are chosen post hoc, which is why the protocol fixes the threshold criterion, the model-comparison test, and the goodness-of-fit test in advance and reports the sample size in the fitted tail alongside every estimate. A specialized but relevant caution from the estimation literature is that maximum-likelihood power-law estimation has large variance when the tail is undersampled, which biases naive fits; the design's multi-year coverage requirement is the first defense, and where the tail is thin the friendship-paradox-style variance-reduction logic flags the undersampling rather than papering over it [\[86\]](#ref-86).

## 6.4 The pre-registered decision rules

Stated exactly as they will be applied, the decision rules below are the prospectus's acceptance rule made operational. They are fixed before estimation so that the verdict is a function of the data and the rule alone.

The wait-time-tail clause of H1 is accepted if and only if two conditions both hold. First, the likelihood-ratio test of the heavy-tailed candidate (power-law, log-normal, or generalized Pareto) against the exponential null prefers the heavier model at the pre-set significance level, with the preference statistically distinguishable from a tie. Second, the generalized-Pareto shape parameter estimated by peaks-over-threshold is significantly positive (`xi > 0`) under the chosen and the Bayesian-averaged threshold treatments. If the likelihood-ratio test cannot distinguish the heavier candidate from the exponential, or if the estimated shape parameter is statistically indistinguishable from zero, the null is retained for waits and the wait-time clause fails.

The concentration clause of H1 is accepted if and only if the top-decile loss share \(T_{10}\) is materially above the ten-percent uniformity benchmark, with "materially above" fixed in advance at a pre-registered threshold (an illustrative pre-registration value, stated in the prospectus, is \(T_{10}\) at or above forty percent), and the small-sample-corrected Gini coefficient \(G\) is correspondingly elevated and statistically distinguishable from its uniform-distribution expectation. If \(T_{10}\) sits near ten percent and the corrected Gini is low, the null is retained for concentration and the concentration clause fails.

The contribution as a whole is accepted only if both clauses pass. The conjunction is deliberate and is not weakened: a heavy wait tail without concentrated loss, or concentrated loss without a heavy wait tail, refutes the joint claim that the penalty is *both* heavy-tailed *and* concentrated. The reason for the conjunctive rule is that the two clauses test logically distinct properties (tail behavior of an outcome over requests versus concentration of an outcome over structural cells, as Chapter 1 distinguishes them), and the dissertation's contribution is the conjunction, not either disjunct. Fixing the conjunction now matters because an analyst who reached the data free to accept the contribution on the stronger of the two clauses would have a degree of freedom the pre-registration is designed to remove. The convex load-response of Step five is treated as confirmatory corroboration of concentration rather than as a third gate: a convex curve strengthens a positive concentration verdict and would make a negative one harder to sustain, but the formal acceptance rests on the two clauses above. One point to keep in view is that all thresholds named here as illustrative pre-registration values are placeholders for the form of the rule; the binding values are those recorded in the pre-registration document (Appendix B) before estimation, and they are not revised after seeing the data.

## 6.5 The illustrative queueing simulation

A design-stage plan cannot estimate the tail on data it has not yet touched, but it can demonstrate, on synthetic data generated under known assumptions, that the proposed pipeline recovers the truth when the truth is known and returns the null when the null is true. The simulation specified here serves that purpose alone. It is not a forecast of the DSN and produces no claim about the real network; it is a calibration and false-positive-control exercise whose only output is evidence that the Section 6.3 protocol and the Section 6.4 decision rules behave as intended. Every quantity in it is a synthetic input chosen by the analyst, labeled illustrative, and carries no implication for the real logs.

### 6.5.1 Why an illustrative simulation is part of the plan

The statistical-conclusion-validity threats named in Chapter 5 and in Section 6.3 are the reason a simulation belongs in the plan: heavy-tail fitting can produce false positives when the threshold is chosen post hoc or the tail is undersampled, and the Gini coefficient is biased in small populations of windows [\[4\]](#ref-4), [\[77\]](#ref-77). Resolving these threats by simulation rather than by assertion is the right move because a pipeline whose properties are demonstrated on data with a *known* generating process is the standard way to show that a positive verdict on the real data would mean what the decision rule says it means. The simulation answers two questions the real-data analysis cannot answer about itself. First, the recovery question: if the synthetic wait times are drawn from a known heavy-tailed process, does the protocol recover a positive shape parameter and reject the exponential at the stated rate. Second, the specificity question: if the synthetic wait times are drawn from a genuinely exponential process, does the protocol *retain* the null at the stated rate rather than manufacturing a spurious heavy tail. A pipeline that passed the first test but failed the second would be a pipeline that finds concentration everywhere, and it would be worthless as a test of the contribution. One limit must be stated: the simulation validates the *method*, not the *hypothesis*. It can show that the pipeline would detect a heavy tail if one exists in the real logs and would not invent one if none exists, but it cannot tell us which is the case on the real DSN, which only execution can.

### 6.5.2 The generating model

The synthetic generator is a discrete-event queueing model whose structure mirrors the three heavy-tail routes named in Chapter 2, so that the simulation exercises exactly the mechanisms the design claims to detect. Requests arrive at a synthetic three-complex network according to an arrival process whose burstiness is a tunable parameter: at one extreme the arrivals are Poisson (smooth, the light-tailed reference), and at the other they are clustered on a small set of synthetic geometry windows, reproducing the bursty-arrival route to heavy tails [\[51\]](#ref-51), [\[82\]](#ref-82). Each request carries a synthetic viewing-window deadline, after which it abandons unserved, reproducing the deadline-driven-abandonment route; the patience-time distribution is drawn from the impatient-customer and reneging models so that the abandonment dynamics match the queueing literature rather than an ad hoc rule [\[48\]](#ref-48), [\[49\]](#ref-49), [\[84\]](#ref-84). Service times are drawn from a distribution whose skewness is a tunable parameter, with a minority of high-rate critical-event passes occupying a server far longer than routine cruise passes, reproducing the skewed-service route. The server-allocation discipline is a synthetic priority-and-preference rule that systematically defers a configurable subclass of requests, reproducing the priority mechanism by which an otherwise moderately loaded queue develops a heavy upper tail among the deferred subclass [\[83\]](#ref-83), [\[44\]](#ref-44). The mean offered load is held at a moderate level on purpose, so that any heavy tail the simulation produces arises from burstiness, deadlines, skew, and priority rather than from saturation; this is the operational form of the Chapter 2 claim that moderate average load plus structure, not high average load alone, is the route to a fat tail. The system-dynamics reading of the same structure, in which backlog and unmet-requirement stocks accumulate under delayed feedback, is reproduced by letting synthetic missions adjust their request timing and padding in response to observed backlog, closing the Forrester loop in the generator [\[21\]](#ref-21), [\[62\]](#ref-62), [\[30\]](#ref-30).

### 6.5.3 The simulation protocol and its expected behavior

The protocol sweeps the four tunable knobs (arrival burstiness, deadline tightness, service skew, and the size of the deferred subclass) across a grid from their light-tailed settings to their heavy-tailed settings, and at each grid point it runs the full Section 6.3 fitting protocol and applies the Section 6.4 decision rules to the synthetic wait and loss data. The output is a map from generating assumptions to verdicts. At the light-tailed corner of the grid, where arrivals are Poisson, deadlines are loose, service is near-deterministic, and no subclass is deferred, the protocol should retain the null: the likelihood-ratio test should fail to prefer a heavy candidate over the exponential, the estimated shape parameter should be statistically indistinguishable from zero, and the top-decile loss share should sit near ten percent. At the heavy-tailed corner, where arrivals are clustered, deadlines bind, service is skewed, and a subclass is deferred, the protocol should reject the null: a positive shape parameter, a likelihood-ratio preference for the heavier candidate, and a top-decile loss share well above ten percent. The interior of the grid traces the boundary at which the pipeline crosses from retaining to rejecting the null, and that boundary is itself a deliverable, because it shows how much structure the real logs would need to exhibit before the pipeline would call the tail heavy.

The illustrative values attached to this expected behavior are placeholders for the *form* of the validation output, not estimates and not claims about the DSN. An illustrative target for the specificity test is that at the light-tailed corner the protocol should spuriously reject the null in no more than the nominal false-positive rate of the likelihood-ratio test, which is the property the goodness-of-fit and threshold-selection steps are designed to enforce [\[4\]](#ref-4), [\[6\]](#ref-6). An illustrative target for the recovery test is that at a heavy-tailed grid point generated with a known shape parameter, the protocol should recover a shape estimate whose confidence interval covers the true value, demonstrating that the peaks-over-threshold estimator is unbiased under correct threshold selection [\[54\]](#ref-54), [\[58\]](#ref-58). The corresponding simulation result table is specified-but-unpopulated by design: it has rows for grid points from the light-tailed to the heavy-tailed corner and columns for the recovered shape parameter, the likelihood-ratio verdict, the recovered top-decile share, and the realized false-positive or recovery rate, and its cells are filled only when the simulation is run. The objection this simulation design must survive is that a synthetic generator can be tuned to make any pipeline look good; the mitigation is that the generator's structure is fixed by the Chapter 2 mechanism rather than chosen to flatter the pipeline, and the specificity test at the light-tailed corner is the adversarial case the generator cannot be tuned away from without abandoning the exponential reference itself.

### 6.5.4 What the simulation does and does not license

The simulation licenses one inference and forbids another. It licenses the inference that, *conditional on the real wait and loss data resembling one of the generating regimes*, the pipeline would return the verdict the decision rule intends, with controlled false-positive and recovery rates. It forbids the inference that the real DSN data *do* resemble any particular regime, because that is precisely the empirical question the design exists to answer on real logs and the simulation contains no real-log information. The reason for this strict boundary is that a simulation calibrated by the analyst can demonstrate method validity but cannot substitute for data; stating it openly follows from the chapter's standing refusal to let a design-stage artifact masquerade as a finding. The simulation is, in the terms of the dissertation's argument, evidence that the intervention addresses the mechanism (the pipeline detects the structure the theory names) and that the residual risk is manageable (false positives are controlled), but it is silent on whether the problem, in its concentrated form, is present in the real network.

## 6.6 Expected findings, illustrative and not computed
What follows describes the form a positive result would take if the structural mechanism of Chapter 2 holds on the real logs. Every magnitude in it is an illustrative placeholder, labeled as such, chosen to show the shape of a positive finding. None has been computed. The DSN scheduling logs have not been analyzed, no distribution has been fitted, and no concentration coefficient exists. The result tables referenced below are, by design, specified-but-unpopulated: the chapter fixes their structure and leaves their cells empty until the plan is executed.

### 6.6.1 The expected wait-time result

The mechanism predicts, and the design is built to test, a wait-time survival curve that declines slowly in its tail rather than dropping off at the exponential rate. Under a positive result the stratified Kaplan-Meier curves would separate at long waits, with the high-load, contested-band, and critical-phase strata exhibiting visibly fatter tails than the low-load cruise stratum. The formal tail fit would, under a positive result, return a generalized-Pareto shape parameter greater than zero; an illustrative value, offered only to show the form and not as an estimate, is a shape \(\xi\) in the neighborhood of 0.3 to 0.5, which would correspond to a tail heavy enough that the mean wait understates the exposure during the worst windows. The likelihood-ratio test would, under a positive result, prefer a power-law or log-normal upper tail over the exponential at the pre-set significance level. The corresponding result table (specified, unpopulated) has rows for the exponential, log-normal, power-law, and generalized-Pareto candidates and columns for the fitted parameters, the likelihood-ratio statistic against the exponential, the goodness-of-fit p-value, and the fitted-tail sample size; its cells are empty by design and will be filled only by execution.

The basis for expecting this form, rather than asserting it, is the three concurrent queueing routes of Chapter 2, each independently associated in its literature with a non-exponential wait tail [\[83\]](#ref-83), [\[51\]](#ref-51), [\[80\]](#ref-80). It is stated as an expectation and not a finding because of the design-stage posture: the mechanism makes the heavy tail the structurally favored outcome, but whether the logs realize it is the empirical question, and the confidence in the empirical claim is undetermined until the fit is run. The objection the expectation must survive is that the wait tail could be statistically indistinguishable from exponential on the real data, in which case the wait-time clause fails and the null survives for waits; this outcome is fully reportable and is not designed out.

### 6.6.2 The expected concentration result

Under a positive result, lost downlink would concentrate on a minority of geometry-phase windows. The Lorenz-type curve of cumulative loss against window rank would bow sharply away from the line of equality, and the top decile of windows would carry far more than the ten percent that uniformity predicts. An illustrative top-decile share, offered only to show the form, is a \(T_{10}\) on the order of one-half to two-thirds of total lost downlink, against the ten percent of the uniform benchmark, with a correspondingly elevated small-sample-corrected Gini coefficient. The carrying windows that the design anticipates would be the conjunction-driven viewing-overlap windows, the critical mission-event windows, and the high-load concurrency intervals named in the causal mechanism of Chapter 2. The result table (specified, unpopulated) lists the top-ranked windows with their geometry-phase-complex-band identifiers and their \(D_w\) shares, with the Gini coefficient (corrected and uncorrected) and the \(T_{10}\) reported with standard errors; its cells are empty by design.

The basis for expecting concentration is Forrester's structural argument that looped, delayed feedback among locally optimizing missions piles contention onto shared windows faster than the relieving feedback can act, an argument reinforced by the supply-chain and operations-management demonstrations that such feedback produces amplification and instability rather than smoothing [\[21\]](#ref-21), [\[62\]](#ref-62), [\[63\]](#ref-63). It is stated as expectation, again, because of the design-stage posture. One caution is the small-sample issue: in a thin population of windows the Gini coefficient is biased downward [\[77\]](#ref-77), so a *low* uncorrected Gini would not by itself license the null, and the corrected coefficient and the more transparent \(T_{10}\) carry the verdict. The objection the expectation must survive is that an apparent concentration could be an artifact of a few atypical missions; the leave-one-mission-out robustness check and the mission fixed effects of Step four address this, and a concentration that vanishes when any single mission is removed would not count as support for H1.

### 6.6.3 The expected driver and load-response results

Under a positive result, the pass-loss regression would show higher loss probability in the conjunction-driven viewing-overlap windows, in the most contested band, and at the highest concurrent-load quartile, with critical mission-phase windows carrying elevated loss conditional on load. In the Cox model, the concurrent-load covariate would carry a negative allocation-hazard coefficient (lower hazard, longer wait), the expected sign for a driver of contention. An illustrative ordering, offered only to show the form, is that the highest-load quartile would exhibit a materially higher loss probability than the lowest, with the conjunction-overlap geometry and the contested band adding to that effect; the magnitudes are placeholders, not estimates. The driver result table (specified, unpopulated) has rows for each covariate and columns for the Cox hazard ratio, the logistic odds ratio, the GLM coefficient on lost-downlink magnitude, and their confidence intervals; its cells are empty by design.

Under a positive result, the load-response curve would be convex: expected lost downlink would rise faster than linearly as concurrent load increases, and the quadratic or spline term in load would carry a significant convex coefficient. This convexity is the Taleb fragility signature [\[28\]](#ref-28), [\[29\]](#ref-29), and its illustrative form is an accelerating curve whose slope steepens in the high-load region rather than a straight line. The basis for expecting convexity is that the same delayed-feedback structure that concentrates loss on shared windows also makes the marginal request added at high load more likely to be lost than the marginal request added at low load, which is acceleration. The curve is the externally valid object because it, and not the average satisfaction rate, predicts how the penalty would scale into the higher-load crewed-exploration era the data do not yet contain [\[17\]](#ref-17), [\[31\]](#ref-31). The objection it must survive is that apparent convexity could be driven by a handful of extreme-load points; the curve is therefore reported with and without the most extreme load decile, and a convexity that depends entirely on those points would be downgraded.

### 6.6.4 The expected negative result, stated symmetrically

The design does not presuppose the alternative, and the negative result is described with the same specificity as the positive one so that it is genuinely reportable. If the wait tail were statistically indistinguishable from exponential under the likelihood-ratio test, if the estimated generalized-Pareto shape parameter were indistinguishable from zero, if the top-decile loss share \(T_{10}\) sat near ten percent and the corrected Gini were low, and if the load-response curve were linear or concave, then the null would survive on every clause and the contribution would be refuted. This is a concrete, achievable data outcome, not a rhetorical concession. Its basis is that the queueing routes named in Chapter 2 are structurally present but not logically guaranteed to dominate; an exceptionally effective scheduler, a demand profile smoother than the mechanism assumes, or a priority discipline that does not in fact defer a stable subclass could each produce a light-tailed, uniform penalty. The negative result is fully reportable because of the falsifiability requirement that defines the contribution as scientific: a design under which the null could not surface would not be a test. The strategic reading of a negative result, developed in Chapter 7, is itself useful: a uniform, light-tailed penalty would justify broad rather than targeted capacity expansion, which is a real and actionable planning conclusion.

## 6.7 The event-study and loss-profile interpretation

The five estimation steps and the simulation produce distributions, coefficients, and curves, but a planner does not act on a shape parameter. A planner acts on a localized, interpretable profile of when and where the network loses science. The pre-registered interpretive protocol here converts those statistical outputs into the event-study and loss-profile readings that make the result decision-usable, rather than leaving the door open to read patterns into the data after the fact.

### 6.7.1 The window-profile reading

The first interpretive object is the window profile: the rank-ordered list of geometry-phase windows produced by Step three, annotated with the geometry, phase, complex, and band that define each window and with the share of total lost downlink it carries. Under a positive concentration verdict, this profile is the localization deliverable: it names the conjunction-driven viewing-overlap windows, the critical mission-event windows, and the high-load concurrency intervals that the mechanism predicts would dominate, and it attaches to each a measured loss share rather than a conjecture. The profile counts as interpretation rather than raw output because the window definition itself encodes the mechanism: the cells are constructed from the geometry and phase covariates that Chapter 2 names as the collision points of locally optimal requests, so a concentration of loss onto a small set of cells is not a bare statistical fact but a fact already aligned with the causal story. The profile is read causally-suggestively rather than causally-definitively because of the boundary stated in Section 6.8: the profile localizes loss and shows it falls on the windows the mechanism names, which is consistent with the mechanism but does not prove it generated the pattern. One condition is that the profile's interpretability depends on the windows being defined before estimation, not gerrymandered afterward to maximize apparent concentration; the window discretization is therefore fixed in the pre-registration document (Appendix B), and a post-hoc redefinition that increased \(T_{10}\) would be reported as a separate exploratory analysis, never as the confirmatory result.

### 6.7.2 The mission-phase event study

The second interpretive object is an event study around critical mission phases. Because the design records each request's mission-phase indicator (launch, maneuver, encounter, entry-descent-landing versus cruise), the realized wait and loss can be profiled as a function of time relative to a critical-phase event, producing the event-study trace that operational planners read most naturally: how does pass-loss behave in the days before and during an encounter or a maneuver compared with the cruise baseline. Under a positive result, the trace would show elevated loss conditional on load in the critical-phase windows, with the elevation concentrated in the narrow interval when the phase binds and the viewing geometry compresses. The basis for the event-study framing is that the mission-phase windows are the cells where the navigation-and-guidance stakes are highest, since a radiometric tracking pass lost during a trajectory-correction or encounter phase degrades the orbit-determination solution exactly when it matters most, the coupling established in Chapter 1. The event-study trace counts as more than description because it ties the abstract concentration measure to the operational moment a planner cares about: a high \(T_{10}\) is informative, but an event-study trace showing that the carrying windows coincide with maneuver and encounter phases is what makes the finding actionable for navigation planning. The mechanism reading is explicit and bounded: the deadline-driven-abandonment route of Chapter 2 predicts that loss should spike precisely where the viewing window is tightest and the phase is least deferrable, which is the critical-phase interval, and the event study is the test of that prediction at the level of the operational event [\[48\]](#ref-48), [\[49\]](#ref-49). The objection the event study must survive is that elevated critical-phase loss could reflect that the most valuable science is *requested* in those phases rather than *lost* to contention there, the high-value-by-selection alternative; the criticality-weighted construct and the within-mission identification are the partial remedies, and where the volume-based trace and the criticality-weighted trace diverge, both are reported.

### 6.7.3 The survival-profile reading and its operational translation

The third interpretive object is the stratified survival profile from Step two, read not as a statistical curve but as a service-level statement. The Kaplan-Meier survival of the wait, stratified by load quartile and band, translates directly into the operational quantity "what fraction of requests of this type are still waiting after this much time," which is the language of service-level agreements and mission planning. Under a positive result, the divergence of the stratified curves at long waits is the operational signature that the high-load, contested-band requests experience a service level whose worst case is far worse than the mean, the Extremistan reading from Chapter 2 in which the average wait understates the exposure during the worst windows. The basis for this translation is that survival functions are the standard interpretive bridge between time-to-event statistics and operational service levels [\[65\]](#ref-65), [\[89\]](#ref-89), and it is appropriate here because a planner negotiating a mission's downlink requirements needs the tail of the wait, not its mean, to size the margin the mission must carry. One condition is that the survival profile is conditional on the studied epoch's mission mix and is not a forecast; the load-response curve of Step five, not the survival profile, is the object that extrapolates to the higher-load era, and the two are reported together so that the static service-level reading and the dynamic scaling reading are not confused.

### 6.7.4 Reading a null profile

The interpretive protocol is symmetric, and a null result has its own profile reading. If the concentration verdict is negative, the window profile would be flat: cumulative loss would track window rank close to the line of equality, the top decile would carry near ten percent, and no small set of geometry-phase cells would stand out. If the event study were null, critical-phase loss would not exceed the cruise baseline once load is controlled. If the survival profile were null, the stratified curves would coincide, indicating a uniform service level across load and band. The null profile is specified in advance for the same falsifiability requirement that governs the decision rules: an interpretive protocol that could only render a concentrated picture would be reading concentration into noise. The null profile is taken seriously because of its operational consequence, developed in Chapter 7: a flat window profile, a null event study, and coincident survival curves would jointly indicate that the penalty is uniform, which directs a planner toward broad capacity expansion rather than targeted intervention, a real and actionable conclusion rather than a failed result.

## 6.8 What a robust result would and would not establish

A design-stage plan is only honest if it states in advance what its eventual output can and cannot support. Fixing that boundary here is itself part of the pre-registration: it prevents the post-hoc inflation of a descriptive finding into a causal one.

A robust positive result would establish three things and no more. It would establish, descriptively, that the science-throughput penalty is heavy-tailed in wait and concentrated in loss, because those are exactly the properties the two clauses test against fixed thresholds. It would establish, by localization, *which* geometry-phase windows carry the loss, because the concentration step ranks the windows and the driver regression associates loss with named covariates. And it would establish, through the convex load-response, that the penalty scales worse than linearly with load, which is the property a planner needs for the higher-load era the data do not contain. These three deliver the argument the dissertation set out to make: the problem is real and material (Chapters 1 and 4), the distributional method addresses the mechanism the theory names (Chapters 2 and 5), and it beats the status-quo mean satisfaction rate, which cannot distinguish uniform from concentrated by construction (Chapter 3). The residual risk is bounded by the pre-registered decision rules, the goodness-of-fit tests, and the small-sample corrections specified above, which completes the chain of reasoning.
A positive result would *not* establish the causal claim that the Forrester feedback structure *produces* the concentration. The concentration step is descriptive, and the driver regression is conditional-associational under a stated identifying assumption; neither is a structural estimate of the feedback loop. The convex load-response curve is the closest the cross-sectional design comes to a causal signature, and even it is consistent with explanations other than feedback-driven piling, such as high-value science being requested precisely in the contested windows. This last alternative, that the loss is high-*value* by selection rather than high-*volume* by contention, is not resolved by the volume-based concentration measure alone. The criticality-weighted construct of Chapter 4 and the within-mission identification of Chapter 5 are the partial remedies, and where mission records do not permit full criticality weighting the claim is stated in data-volume units with the value caveat attached. The boundary is drawn here because the design is a distributional characterization, not a structural identification of a dynamic feedback system, which would require either a longitudinal intervention or a calibrated system-dynamics simulation beyond the present scope. The boundary is stated plainly, rather than letting the reader infer causation from concentration, because of the dissertation's standing confidence posture: the mechanism is theoretically well supported and the description would be empirically established, but the causal link between them remains theory, and the honest report says so. The single sentence that closes the boundary is this: the plan can measure the shape of the penalty and localize it, and it can show that the shape is consistent with the named mechanism, but it cannot, from cross-sectional logs alone, prove that the mechanism is what made the shape, and it does not claim to.

A complete, ordered, pre-registered pipeline; a fixed decision rule that binds the verdict to the data before the data are seen; a symmetric account of the positive and negative results the pipeline could return, with every magnitude marked illustrative and every result table specified but unpopulated; and an explicit boundary on what even a positive result would license: these are what a design-stage analysis plan owes its reader, and they are what this chapter delivers. The next chapter takes the two possible verdicts, concentrated or uniform, and develops the operational consequences of each: the three levers of capacity, policy, and demand-shaping under concentration, and the case for broad expansion under uniformity, tying each back to the causal mechanism rather than to any architecture vocabulary, consistent with the scope decision stated in Chapter 1.


# Chapter 7: Discussion

## 7.0 The chapter's answer, stated first

The shape of the science-throughput penalty is not a descriptive curiosity. It is the variable that decides where NASA and the Jet Propulsion Laboratory should spend constrained aperture, scheduling-policy effort, and downlink-requirement negotiation. This chapter's thesis is that the design developed in Chapters 4 through 6 is decision-relevant under **both** of its possible outcomes, and that the two outcomes prescribe opposite portfolios of action rather than different intensities of the same action. If the analysis returns H1, that the request-to-allocation wait time and the lost-downlink magnitude are heavy-tailed and concentrated on a minority of orbital-geometry and mission-phase windows, then the highest-return interventions are surgical: aperture, discipline changes, and demand shaping aimed at the specific windows the estimation localizes. If the analysis returns H0, that scheduling friction is roughly uniform and light-tailed, then surgical interventions buy little, and the rational response is broad capacity expansion together with a recognition that the aggregate satisfaction rate is, in that world, an adequate planning summary. Either result is a usable input; neither is a null in the colloquial sense of "nothing learned." That symmetry is the property that makes the contribution scientific rather than advocacy, and it organizes everything that follows.

The chapter is organized to discharge five obligations the prospectus places on it. First, it interprets the implications under both outcomes, refusing to treat H1 as the foregone conclusion. Second, it traces the theoretical contribution back to each of the three anchor frameworks, queueing theory, Forrester's system dynamics, and Taleb's fat-tails-and-fragility program, so that a confirmed or refuted result feeds back into the bodies of thought that generated the prediction. Third, it states the policy and mission implications for NASA, JPL, and the missions that depend on the Deep Space Network (DSN), keyed to Meadows's ranking of leverage points [\[26\]](#ref-26) so that the levers are ordered by structural strength rather than by convenience. Fourth, it engages the rival explanations in full, not as a defensive checklist but as live alternatives whose defeat is part of what makes the claim credible. Fifth, it states the external-validity boundary explicitly, arguing that the load-response curve, not any single satisfaction rate, is the externally valid object the crewed-exploration era requires. The confidence posture throughout is design-stage: the mechanism for H1 is theoretically well-supported, but whether H1 holds on the real logs is untested and is exactly the empirical question this design exists to answer.

A word on what the chapter does not do. It does not force architecture-traceability vocabulary onto a queueing study. The DSN is a real fielded capability, but this dissertation specifies no new system, capability, or data-or-service exchange; it characterizes the statistical shape of a penalty that an existing capability already imposes. The decision-relevance is therefore carried by the causal mechanism and by the lever analysis in Section 7.1, which map a strategic objective (recover the most science return per dollar) to a planning choice (broad versus targeted intervention) without a DoDAF or Business Enterprise Architecture layer. Inventing such a layer here would be placeholder vocabulary with no referent.

## 7.1 Implications under a heavy-tail-and-concentration result (H1)

If H1 holds, the operational implication is that a small, targeted portfolio of interventions aimed at the carrying windows recovers a disproportionate share of lost science return, and this targeting dominates uniform capacity expansion on a return-per-dollar basis.

This rests on the structure of the result H1 describes, not yet on any executed estimate. H1 is the conjunction of two measured properties: a heavy upper tail in the wait-time and pass-loss distributions (a generalized-Pareto shape parameter `xi > 0`, an exponential rejected by likelihood-ratio test against a heavier candidate [\[4\]](#ref-4), [\[5\]](#ref-5), [\[6\]](#ref-6)) and a concentration of lost downlink onto a minority of geometry-phase windows (a top-decile window share \(T_{10}\) materially above the ten percent uniformity benchmark, with a correspondingly elevated Gini coefficient \(G\) [\[76\]](#ref-76), [\[78\]](#ref-78)). If those two properties co-occur, then by construction the loss is localizable: there exists a small set of windows, indexed by orbital geometry, band, complex, and mission phase, that carries the majority of the lost-downlink mass \(D_w\). A portfolio aimed at that set acts on the majority of the loss while spending on a minority of the calendar.

What connects "loss is concentrated" to "targeted intervention dominates" is the elementary economics of marginal return under a skewed loss distribution: when the marginal lost-downlink recovered per unit of intervention is far higher on the carrying windows than on the median window, allocating the next dollar to the carrying windows yields more recovered science than spreading it uniformly. This is the same logic that makes targeted reinsurance efficient when loss severity is generalized-Pareto distributed [\[54\]](#ref-54), transposed from insurance loss layers to downlink loss windows. The logic holds only if the carrying windows are stable enough to be targeted, which is itself a testable property and is addressed below as an objection.

Treating the carrying windows as the right object of intervention, rather than the network mean, follows from Meadows's ranking of intervention points [\[26\]](#ref-26), which places the structure of information flows and the rules of the system well above the adjustment of numerical parameters. Adding aperture uniformly is, in Meadows's taxonomy, a low-return parameter change: it raises a constant in the supply equation without altering the loop structure that concentrates contention. Reshaping the rules that govern which requests are deferred, and reshaping the information feedback that drives missions to pile requests onto shared windows, are higher-return moves. The Forrester mechanism developed in Chapter 2 explains why those higher-return moves exist to be made: contention concentrates because looped, delayed feedback among locally optimizing missions piles requests onto the same windows, so an intervention on that feedback, not merely on the antenna count, is available.

The claim is advanced at moderate design-stage confidence. The mechanism that predicts concentration is strong and triangulated across three frameworks, but the magnitude of the targeting advantage, how much more science a targeted dollar recovers than a uniform dollar, is unestimated and depends on the realized \(T_{10}\) and on the cost structure of each lever, neither of which this design has yet measured. Confidence would rise to high if the estimation returned a large \(T_{10}\) (illustratively, a top-decile share on the order of half to two-thirds, the placeholder magnitude used in Chapter 6 and labeled illustrative there) together with carrying windows that recur across cycles. Confidence would fall toward low if \(T_{10}\) were only modestly above the benchmark or if the carrying windows shifted unpredictably between cycles.

The claim fails if the carrying windows, though concentrated in any single cycle, are not the *same* windows across cycles, because then there is no stable target to aim at and the apparent concentration is a moving shadow rather than a fixed feature. This objection is taken seriously, and it is the reason the coverage requirement in Chapter 4 demands a multi-year span that includes several cycles of the recurring high-contention windows: stability across cycles is precisely what that coverage is designed to test. If the windows are stable, the objection is met and targeting is justified; if they are not, the H1 result would still establish heavy-tailedness but would weaken the targeting prescription, a distinction the discussion preserves rather than papers over.

### 7.1.1 The three levers, ordered by leverage

Granting the claim above, three levers follow, and Meadows's ranking [\[26\]](#ref-26) orders them from the lowest-leverage parameter adjustment to the highest-leverage rule change. Naming them in that order is deliberate: it resists the institutional default of reaching first for the most expensive and least structural option.

**Lever one: capacity, including arraying, as the parameter adjustment.** The most direct response to concentrated contention is to add serving capacity at the carrying windows: more antenna time on the specific complexes, bands, and epochs the analysis localizes. Within the existing plant, antenna arraying offers capacity without new large-aperture construction by combining the signals of several smaller antennas to synthesize a larger effective aperture, a technique with a long DSN heritage [\[71\]](#ref-71). The mechanism by which arraying relieves a carrying window is concrete: a window whose contention is driven by a high-rate critical pass that occupies a 70-meter antenna can, in principle, be served by an array of 34-meter antennas, freeing the single large aperture for a concurrent request and thereby raising the instantaneous service rate during exactly the interval when burstiness has spiked the arrival rate. This is a parameter change in Meadows's sense, the lowest-leverage of the three, and the discussion flags it as such: it raises supply without touching the feedback that generates the demand spike. It is nonetheless the lever most readily costed and most defensible to a capacity-planning sponsor, which is why it is named first even though it is structurally weakest.

**Lever two: scheduling discipline, as the rule change.** The heavy wait tail that H1 would establish is, in part, a product of a priority-and-preference discipline that systematically defers an identifiable subclass of requests. The queueing-plus-scheduling literature is explicit that the choice of queue discipline shapes the realized wait distribution, and that disciplines which defer a subclass to protect aggregate throughput convert moderate average load into a heavy conditional tail for the deferred subclass [\[9\]](#ref-9). The mechanism for relief is therefore to redesign the discipline so that the deferred subclass is protected: for instance, by reserving a guaranteed minimum service rate for requests that would otherwise be repeatedly bumped, an approach analogous to the delay-bound-based fairness that separates heavy-tailed from light-tailed flows in communication scheduling [\[47\]](#ref-47). Feedback queueing models show that quantum-controlled disciplines can be tuned to bound the wait of the worst-served class rather than only the mean [\[44\]](#ref-44). This is a higher-leverage move than adding aperture because it changes the rule that allocates a fixed supply rather than changing the supply, and it can recover tail science return at near-zero hardware cost. Its risk is that protecting the deferred subclass redistributes wait onto the previously favored subclass, so the lever must be evaluated against the full distribution of waits, not against the tail alone.

**Lever three: demand shaping, as the feedback intervention.** The highest-leverage lever acts on the Forrester feedback itself. Missions submit requests early, inflate requested durations to hedge against being cut, and escalate priority for critical phases; each of these is locally rational, and in aggregate they are a reinforcing pressure that piles requests onto the shared windows everyone wants. The system-dynamics literature on order stability shows that this class of self-interested hedging is the same mechanism that produces the bullwhip effect in supply chains, where coordination risk under uncertainty about others' behavior amplifies order variance upstream, and that a coordination intervention, holding a buffer that reduces the incentive to hedge, can damp the oscillation [\[63\]](#ref-63). Transposed to the DSN, demand shaping means negotiating mission downlink requirements and request timing so that the hedging feedback does not concentrate on the carrying windows: for example, by giving missions a credible early commitment that reduces their incentive to pad, or by smoothing request submission across the geometry windows rather than letting it cluster. This is the strongest lever in Meadows's ranking because it changes the information feedback and the rules together, but it is also the hardest to implement, because it requires coordinated behavior change across independent mission teams rather than a unilateral action by the network operator.

**Synthesis of the levers.** The three levers are not substitutes to be chosen among but a ladder to be climbed in order of structural strength: capacity buys time, discipline redistributes the fixed supply toward the underserved tail, and demand shaping attacks the feedback that generates the concentration in the first place. The decision-relevant point for NASA and JPL is that under H1 the return on the higher rungs is multiplied by the very concentration the result establishes, because a feedback intervention that relieves a carrying window relieves a disproportionate share of the total loss. Each lever is, finally, itself testable: the design can be re-run on post-intervention logs, and a successful intervention should flatten the tail, lower \(T_{10}\), and reduce the convexity of the load-response curve. That re-runnability is what converts the discussion from prescription into a closed evaluation loop.

## 7.2 Implications under a uniform result (H0)

If H0 holds, the targeting prescription of Section 7.1 is not justified, and the rational response is broad capacity expansion together with continued use of the aggregate satisfaction rate as an adequate planning summary; this is a substantive, decision-relevant finding, not a failure of the study.

H0 is the joint statement that the wait-time tail is statistically indistinguishable from exponential (the likelihood-ratio test does not prefer a heavier candidate; the generalized-Pareto shape parameter is not significantly positive [\[4\]](#ref-4), [\[6\]](#ref-6)) and that the top-decile window share \(T_{10}\) sits near the ten-percent uniformity benchmark, with a low Gini coefficient \(G\) [\[76\]](#ref-76). Under that conjunction, there is by construction no small set of windows carrying a majority of the loss: lost downlink is spread thinly across requests and times. The claim is therefore internal to the definition of H0; if loss is uniform, there is no carrying window to target.

The reasoning is the same marginal-return logic as in 7.1, run in reverse. When the marginal lost-downlink recovered per unit of intervention is roughly equal across windows, no allocation of the next dollar dominates any other on a recovery basis, so the only way to recover more science is to raise the floor everywhere, which is uniform capacity expansion. In a uniform world the network mean is a sufficient statistic for the loss, because a light-tailed distribution is well summarized by its mean and the sample does not undersample the tail. This is the Mediocristan case in Taleb's vocabulary [\[27\]](#ref-27): the mean and variance are stable, no single window dominates the aggregate, and the historical record is a reliable guide to the future loss.
This outcome is consistent with the queueing result that not all queues produce heavy tails. Multiserver queues with phase-type arrival and service distributions have asymptotically exponential waiting-time tails [\[46\]](#ref-46), and heavy-traffic analyses of many-server systems show that under balanced load and abandonment the stationary queue can be well-behaved [\[43\]](#ref-43), [\[45\]](#ref-45). If the DSN's realized arrival and service processes happen to fall in this light-tailed regime, despite the three heavy-tail routes the theory identifies as available, then exponential waits are what the queueing literature predicts, and H0 is the theoretically coherent outcome rather than an anomaly. The design does not stack the deck for H1. It makes H0 a live and theoretically grounded possibility.

This claim is advanced at moderate confidence, with an asymmetry the discussion is obliged to flag. Taleb's precautionary reasoning [\[27\]](#ref-27) holds that the cost of falsely assuming thin tails is greater than the cost of falsely assuming fat tails, because thin-tail planning that turns out wrong underestimates a real exposure. Accepting H0 therefore carries a residual risk that the study has under-observed the tail: a multi-year record can still be short relative to the recurrence interval of the worst windows. Confidence in H0 is thus conditioned on the coverage having been sufficient to observe the tail had one existed, which is why Chapter 4's coverage requirement and Chapter 6's goodness-of-fit and threshold-stability diagnostics are load-bearing for an H0 conclusion specifically, not only for an H1 conclusion.

The H0 claim is undercut if the apparent uniformity is an artifact of aggregation. If loss is concentrated within fine geometry-phase cells but the discretization used to define windows is too coarse to resolve the concentration, then a genuinely heavy-tailed system can present as uniform. The design guards against this by varying the window discretization in sensitivity analysis and by testing the wait-time tail at the request level, where no window aggregation intervenes. If the request-level tail is also exponential, the objection is met and H0 stands on the finest available resolution. If the request-level tail is heavy while the window-level concentration is low, the result is mixed and is reported as such rather than forced into either box.

The H0 discussion matters because a dissertation that could only interpret one of its two outcomes would be advocacy wearing the costume of inquiry. The design is built so that H0 yields a clean, actionable prescription, broad expansion, trust the mean, of equal standing to the H1 prescription. That both prescriptions are usable is the strongest single argument that the contribution is falsifiable in the demanding sense the prospectus claims for it.

## 7.3 The theoretical contribution back to each anchor

A design-stage dissertation cannot return empirical findings to its anchor frameworks, but it can return a sharpened, testable proposition and an explicit account of what a confirmation or refutation would mean for each body of thought. This section discharges that obligation framework by framework.

### 7.3.1 Back to queueing theory

The contribution to the queueing anchor is the identification of the DSN as a system in which three classical heavy-tail routes are present simultaneously and by construction, and the framing of an empirical test of whether their joint presence produces the heavy waits the theory permits. Queueing theory establishes that deadline-driven abandonment [\[48\]](#ref-48), [\[49\]](#ref-49), bursty or self-similar arrivals [\[51\]](#ref-51), [\[52\]](#ref-52), and skewed service requirements each can convert moderate average load into a heavy upper tail of waits, and that the choice of discipline mediates which subclass bears the tail [\[9\]](#ref-9), [\[44\]](#ref-44). What the theory does not settle, and what no prior space-operations paper has measured, is whether a real deep-space tracking network exhibits these tails in its realized request-to-allocation waits. The dissertation returns to queueing theory a domain instance: a fielded multiserver system with hard viewing-window deadlines (the target is visible from a complex only for a bounded interval, so an unserved request is lost, not merely delayed), with arrival burstiness driven by the coincidental good placement of many targets, and with service-time skew driven by high-rate critical passes. A confirmed H1 would be a domain confirmation that the joint-route prediction holds in deep-space operations. A confirmed H0 would be the more surprising and arguably more informative result, that a system with all three routes available nonetheless produces light-tailed waits, which would prompt the question of what discipline or structural feature suppresses the tails the theory expects. Either way the anchor gains an empirically anchored test case it presently lacks.

This is, the chapter notes plainly, a transfer-of-mechanism argument rather than a citation to a prior deep-space result, and it is flagged as such for the examiner. The deadline-abandonment and self-similarity results are drawn from operations-research and telecommunications settings [\[48\]](#ref-48), [\[49\]](#ref-49), [\[51\]](#ref-51), [\[52\]](#ref-52), and the mapping onto DSN viewing-window deadlines is argued by construction in the theoretical framework, not borrowed from a space-domain precedent. The novelty and the thinness are the same fact viewed from two sides: no one has done this transfer for the DSN, which is why it is a contribution and also why it must be defended rather than assumed.

### 7.3.2 Back to Forrester and system dynamics

The contribution to the Forrester anchor is a falsifiable operationalization of the counterintuitive-concentration claim in a setting where the stocks, flows, and delayed feedback are observable in operational logs. Forrester's central proposition is that system behavior is dominated by loop structure and delay rather than by the intentions of the actors, and that this produces concentration that local reasoning does not anticipate [\[21\]](#ref-21), [\[23\]](#ref-23). The DSN renders this proposition testable because its stocks (the backlog of unserved requests, the accumulated unmet downlink requirement per mission) and its flows (request arrival rate, pass allocation and execution rate) are recorded, and because the feedback (missions responding to backlog by submitting earlier and padding more) is visible in the request stream. The concentration test, \(T_{10}\) and \(G\) over geometry-phase windows, is a direct measurement of whether the loop structure piles loss onto shared windows as Forrester's lens predicts. A confirmed H1 with stable carrying windows would be a clean operational instance of counterintuitive concentration; the order-stability and bullwhip literature [\[63\]](#ref-63), and the broader operations-management synthesis of system dynamics [\[62\]](#ref-62), would gain a ground-station-scheduling exemplar alongside their supply-chain ones. A confirmed H0 would be evidence that, in this system, the feedback does not concentrate, which would be a counterexample worth understanding: perhaps the multi-stage DSN scheduling workflow [\[10\]](#ref-10), [\[16\]](#ref-16), with its long-range forecasting and mid-range negotiation, damps the hedging feedback before it can concentrate, in which case the workflow itself is a coordination-stock intervention of the kind the order-stability work identifies as stabilizing [\[63\]](#ref-63).

The design's limit, returned honestly to the anchor, is that a cross-sectional measurement of concentration tests the *consequence* the Forrester lens predicts (concentrated loss, convex load-response) but does not directly observe the *loop* operating in time. The convex load-response curve is the closest the design comes to a dynamic signature, and even it is a comparative-static reading of loss against load rather than a traced feedback loop. The dissertation therefore returns to system dynamics a partial test: it can confirm or refute the predicted concentration, but attributing that concentration to the specific feedback loop, rather than to some other source of skew, remains beyond the cross-sectional design and is named as future work requiring a dynamic, longitudinal model of the request-and-allocation process.

### 7.3.3 Back to Taleb and the fat-tails program

The contribution to the Taleb anchor is twofold and is the most methodologically direct of the three. First, the dissertation adopts and instantiates Taleb's first instruction, do not assume light tails by default; test for them and prefer the heavier-tailed model unless the data reject it, because the cost of falsely assuming thin tails is asymmetric [\[27\]](#ref-27). The estimation protocol, Clauset-Shalizi-Newman maximum-likelihood fitting with goodness-of-fit and likelihood-ratio comparison against the exponential [\[4\]](#ref-4), [\[5\]](#ref-5), [\[6\]](#ref-6), together with generalized-Pareto peaks-over-threshold tail estimation [\[54\]](#ref-54), is the standard implementation of that instruction, applied here to a domain (deep-space scheduling) where the default assumption has been the light-tailed congestion picture implicit in reporting a mean satisfaction rate. Second, the dissertation adopts Taleb's second instruction, characterize the convex second-order response of the system to the dose of the stressor rather than forecasting the stressor [\[28\]](#ref-28), [\[29\]](#ref-29). The load-response curve, expected lost-downlink plotted against concurrent-mission load, is the convexity diagnostic the antifragility program prescribes: a convex (accelerating) response is the signature of fragility, and its presence is independent evidence for concentration because it shows the system's loss accelerating faster than its load. A confirmed H1 with a convex load-response would be a space-operations instance of the regression-to-the-tail phenomenon that the megaproject literature documents for systems with fixed deadlines and tight coupling [\[61\]](#ref-61), two features the DSN shares; the DSN would join the list of fixed-deadline, tightly-coupled systems whose losses follow a power law. A confirmed H0 with a linear or concave load-response would be a Mediocristan case, equally informative, in which the precautionary inversion of the burden of proof is satisfied by the data rather than overridden by it.

What the dissertation returns to the Taleb program is therefore a worked, falsifiable application in a public-infrastructure setting with operational stakes, accompanied by the explicit asymmetry argument: because the cost of falsely assuming thin tails is higher than the cost of falsely assuming fat ones, the design places the burden of proof on H0 and prefers the heavier model unless the data reject it, while still allowing the data to reject it. That is the discipline the anchor demands, made operational on real scheduling logs rather than on a stylized model.

## 7.4 Rival explanations and how the design addresses them

A distributional claim about concentration invites three rival explanations, each of which, if true, would deflate the contribution by attributing the apparent concentration to something other than structural contention. The design addresses each, and naming them here is part of what makes the eventual claim credible rather than an afterthought.

**Rival one: the atypical-mission artifact.** The first rival holds that apparent concentration is driven by a few atypical missions, perhaps one or two high-rate flagship missions whose requests dominate the carrying windows, rather than by a structural property of the network. If true, the concentration would be a feature of the mission roster in a particular epoch, not a durable property of the scheduling system, and the targeting prescription would amount to "serve the flagship," which no analysis is needed to discover. **The design addresses this** through mission fixed effects \(\mu_m\), which absorb time-invariant mission characteristics (instrument data rate, priority class, strategic-padding behavior) so that the load and geometry coefficients are identified from within-mission variation rather than from differences between missions, and through an explicit leave-one-mission-out robustness check that recomputes \(T_{10}\) and \(G\) with each mission removed in turn. If the concentration survives the removal of any single mission, it is not an artifact of that mission; if it collapses when a particular mission is removed, the rival is vindicated for that epoch and the finding is reported with that qualification. Dismissing the rival is thus conditional on the robustness check passing, and the check is pre-registered rather than chosen after seeing the result.

**Rival two: the threshold-choice artifact.** The second rival holds that the heavy tail is an artifact of how the tail-fitting threshold was chosen, since heavy-tail fitting is known to produce false positives when sample sizes are small or thresholds are selected post hoc to flatter the result. **The design addresses this** through the Clauset-Shalizi-Newman goodness-of-fit step [\[4\]](#ref-4), pre-registered threshold-selection diagnostics (mean-residual-life and parameter-stability plots for the generalized-Pareto fit), likelihood-ratio comparison against the exponential null, and a decision rule fixed before estimation. The mechanism by which these defeat the rival is specific: pre-registration removes the analyst's freedom to choose the threshold that maximizes the appearance of a heavy tail, the goodness-of-fit p-value tests whether the fitted model is even an adequate description of the data rather than merely the best of a bad set, and the small-sample literature on the Gini coefficient [\[77\]](#ref-77) warns explicitly that concentration measures are biased in small populations, prompting the small-sample correction that the analysis applies before interpreting \(G\). The rival is a real and well-documented failure mode of heavy-tail empirics, and the design's response is to adopt the exact methodological controls the heavy-tail literature developed to police it.

**Rival three: high-value-by-selection.** The third rival is the most subtle and the most important for the navigation-and-guidance stakes. It holds that loss concentrates on certain geometry windows not because those windows are more contested but because those windows are simply when the most valuable science is requested, so the high lost-downlink there reflects high value by selection rather than high contention. If true, the concentration would be a restatement of "missions ask for a lot during important windows," not a finding about scheduling friction, and intervening on contention would not help because the windows are not over-contested, only over-valued. **The design addresses this** in two ways. First, the within-mission, within-epoch identification separates value from contention: holding the mission and epoch fixed, a given mission faces *different* contention on different requests because of the coincidental load from other missions, variation that is plausibly exogenous to the specific value that mission places on the pass. The load and geometry coefficients are therefore estimated from contention variation that is not the mission's own value signal. Second, the criticality-weighted construct of lost downlink, where mission records permit it, reports the penalty both in raw data-volume units and weighted by mission-declared criticality, so that a window which is high-loss only because it is high-value shows up differently from a window which is high-loss because it is over-contested. The rival is addressed but not fully dispatched at the design stage, because the criticality weights are the least-sourced input (no public citation fully documents per-mission critical-event windows) and the construct-validity robustness may be only partially feasible; this limitation is carried forward honestly rather than minimized.

The cumulative effect of engaging the three rivals is to convert the concentration claim from a bare correlation, loss happens to be high on certain windows, into a defended causal-structural claim, loss is high on certain windows because of contention, holding mission value and roster composition fixed. The causal mechanism developed in Chapter 2 names this chain explicitly: locally optimizing missions, through delayed feedback, pile requests onto shared windows, where deadline-driven geometry, bursty arrivals, and skewed service convert moderate average load into a heavy tail for the deferred subclass. The rival-engagement section is where that mechanism is defended against the three most plausible ways it could be a mirage.

## 7.5 External validity and the crewed-exploration era

The externally valid object of this study is the load-response curve, not any single satisfaction rate, and the crewed-exploration era's penalty is best predicted by that curve; a convex curve implies the exploration-era penalty will be worse than a linear extrapolation of today's average loss.

This rests on the documented and projected shift in the DSN mission mix. The traffic-modeling literature projects that the human-exploration era will add relatively short but tracking-intensive human lunar missions, followed by an increasing cadence of robotic and then human Mars missions, alongside marked growth in the number of robotic spacecraft and large increases in per-mission data rate and data volume [\[17\]](#ref-17), [\[31\]](#ref-31). The heliophysics-portfolio expansion analysis independently quantifies a gap between projected demand and current supply for a specific science program [\[18\]](#ref-18). These sources establish that the future load will be both higher and differently composed than the load in the studied epoch: more high-rate, time-critical traffic, the service-skew and burstiness that the heavy-tail routes feed on.

The reason for preferring the load-response curve over a point estimate is that a curve, unlike a single satisfaction rate, predicts how the penalty scales as load rises, which is the quantity a planner needs for an era the data do not yet contain. A satisfaction rate measured in today's mix answers "how bad is it now"; the load-response curve answers "how bad does it get as load increases," and only the second is extrapolable to a load regime not yet observed. If the curve is convex, then the exploration-era penalty at a higher load is larger than a straight-line projection from today's average, because convexity means loss accelerates with load. The fragility reading is explicit: a convex response to the dose of the stressor is the mathematical signature of a fragile system [\[28\]](#ref-28), [\[29\]](#ref-29), and the megaproject evidence that fixed-deadline, tightly-coupled systems regress to the tail [\[61\]](#ref-61) is a warning that the DSN's fixed viewing-window deadlines and tight inter-mission coupling are the same drivers that produce power-law cost overruns elsewhere. This rests on a methodological principle: Taleb's program insists that one characterize the second-order response rather than forecast the stressor [\[28\]](#ref-28), [\[29\]](#ref-29), precisely because the timing of the next high-contention window is unpredictable while the shape of the loss-versus-load relationship is estimable from existing variation. Reporting the curve rather than a single rate is the operationalization of that instruction, and it is what makes the study's output usable by an exploration-era planner who cannot know the future mission manifest but can know how the system responds to load.
The external-validity claim is advanced at moderate-to-low confidence regarding magnitude and moderate confidence regarding direction. The penalty's shape may be specific to the studied epoch's mission mix, which the design cannot observe in advance. The exploration-era mix will differ, and a curve estimated on today's mix is an extrapolation, not an observation, when applied to tomorrow's. Confidence in the direction of the effect (a convex curve implies worse-than-linear scaling) exceeds confidence in its magnitude (how much worse), because direction follows from the fragility logic while magnitude depends on parameters that will themselves shift with the mix. The claim is therefore conditioned explicitly on the studied mix, and the curve, rather than a single extrapolated number, is reported so that the extrapolation is visible and bounded rather than hidden inside a point estimate.

The external-validity claim fails if the exploration-era mix changes the *shape* of the load-response, not merely its position along the load axis. The estimated curve assumes that the functional relationship between load and loss is stable and that the exploration era moves the system to a higher point on the same curve. If instead the new traffic class (high-rate, hard-deadline crewed passes) introduces a qualitatively different service process, the curve itself could change shape, and the extrapolation would be invalid. The dissertation cannot test this with pre-era data and says so. It offers the curve as the best available externally valid object while naming the regime change that would invalidate it, and it identifies post-era re-estimation as the necessary confirmation.

## 7.6 Relationship to future capacity: optical communications and arraying as alternative supply levers

The supply side of the DSN is not static, and a discussion of implications would be incomplete without situating the contention problem against the capacity trajectory that may alter it. Two developments bear on whether contention will intensify or ease, and the chapter reads both through the same distributional lens.

The first is deep-space optical communications. NASA's Deep Space Optical Communications (DSOC) demonstration, flown on the Psyche mission, established downlink data rates from deep space far above radio-frequency norms, with the flight transceiver designed to support downlink rates from a fraction of a megabit per second up to more than two hundred megabits per second at ranges of roughly 0.1 to 2.7 astronomical units [\[67\]](#ref-67), [\[68\]](#ref-68). The near-Earth Laser Communications Relay Demonstration extends the optical relay architecture in geosynchronous orbit [\[69\]](#ref-69), and the broader free-space-optical literature characterizes both the throughput advantage and the atmospheric-turbulence reliability challenge that ground terminals must overcome through adaptive optics and large-aperture receivers [\[70\]](#ref-70), [\[91\]](#ref-91). The relevance to contention is two-edged, and the distributional framing sharpens the reading. On one side, optical links raise per-pass throughput, which could relieve contention by satisfying a mission's downlink requirement in less antenna-time. On the other, optical ground reception is weather-dependent and site-limited, which introduces a new source of burstiness and deadline pressure, since a cloud-obscured optical window forces traffic back onto the contested radio-frequency network at exactly the moment the optical path was meant to relieve it. Under the H1 reading, optical comms does not automatically flatten the tail; it could relocate the carrying windows to the intervals when optical reception is unavailable and radio-frequency demand spikes. The dissertation's design is the instrument that would tell which effect dominates, by re-estimating the tail and concentration on a mixed optical-and-radio request stream.

The second is antenna arraying, already named as the first lever in Section 7.1. Arraying is a capacity development that operates within the existing radio-frequency plant by synthesizing a larger effective aperture from multiple smaller antennas [\[71\]](#ref-71). Its relationship to the contention problem is that it adds serving capacity precisely where it can be pointed, which under H1 means it can be aimed at the carrying windows rather than spread uniformly. The distributional lens reframes the arraying decision: in a uniform (H0) world, arraying capacity should be added wherever the average load is highest; in a concentrated (H1) world, the return on arraying is highest when it is deployed against the specific complexes, bands, and epochs the concentration analysis localizes. The capacity question, in other words, is not separable from the shape question, and that inseparability is the through-line of the entire discussion: how much capacity to add is a parameter decision, but *where* to add it, and whether to add it at all rather than reshaping discipline and demand, is a decision the shape of the penalty determines.

The chapter closes the supply discussion by returning to the five propositions that carry the argument. The problem is real: the DSN is structurally oversubscribed and forces drops and reductions [\[31\]](#ref-31), [\[33\]](#ref-33), [\[35\]](#ref-35). The problem is material: lost downlink is lost science and, in navigation-critical phases, degraded tracking [\[31\]](#ref-31), [\[34\]](#ref-34). The design addresses the causal mechanism: a queueing-and-survival distributional method measures exactly the tail and concentration the mechanism predicts [\[4\]](#ref-4), [\[9\]](#ref-9), [\[54\]](#ref-54), [\[76\]](#ref-76). It beats the alternatives: a mean satisfaction rate cannot distinguish uniform from concentrated, and the optimization-only literature does not characterize the residual penalty [\[10\]](#ref-10), [\[11\]](#ref-11), [\[32\]](#ref-32), [\[33\]](#ref-33). The residual risk is acceptable: pre-registered decision rules, goodness-of-fit, and fixed-effects identification bound the false-positive risk, and the null is a live, reportable outcome [\[4\]](#ref-4), [\[6\]](#ref-6), [\[27\]](#ref-27), [\[77\]](#ref-77). The point here is that the discussion's implications, under both H1 and H0, rest on those five propositions rather than on the assumption that H1 will hold. Whether the science-throughput penalty is concentrated or uniform, the study converts a known average shortfall into a measured shape, and the shape, not the average, is what tells NASA and JPL where the next dollar of aperture, the next change of discipline, and the next demand negotiation will recover the most science return. That conversion, from average to shape, from advocacy to falsifiable test, from "the DSN is oversubscribed" to "here is the distribution of the penalty and here is what each possible distribution prescribes," is the discussion's contribution, and it is delivered honestly as a design-stage plan whose results are expected and illustrative until the logs are analyzed.


# Chapter 8: Conclusion

## 8.0 The chapter's answer

This dissertation has argued, and this chapter restates as its closing answer, that the science-throughput penalty imposed by Deep Space Network antenna-scheduling contention is most usefully treated not as an average shortfall but as a distribution with a measurable shape, and that the single falsifiable claim worth testing is whether that shape is heavy-tailed and concentrated on a minority of orbital-geometry and mission-phase windows (the alternative hypothesis, H1) or roughly uniform and light-tailed (the null, H0). The contribution of the work is not a finding. No DSN log has been analyzed, no wait-time tail has been fitted, no Gini coefficient has been computed, and every magnitude that appears anywhere in this dissertation is an illustrative placeholder chosen to show the form a result would take, labeled as such at the point of use. The contribution is instead a research design: a queueing-and-survival apparatus, with pre-registered estimators and pre-registered decision rules, capable of converting the realized DSN scheduling and tracking logs into a verdict on the shape of the penalty. What stands at the end of this work, and what this chapter defends, is that the design is sound, that its central question is decision-relevant for NASA and the Jet Propulsion Laboratory whichever way the data fall, and that the design's value does not depend on the alternative being confirmed. If the logs reveal a heavy tail and concentration, the work localizes where constrained aperture, scheduling policy, and demand negotiation recover the most science per dollar. If the logs reveal uniformity, the work justifies broad rather than targeted capacity expansion and retires a plausible but unconfirmed structural conjecture. Either outcome is a usable answer, and the design is built so that both are reachable.

This is the posture the dissertation has held from its first page, and the conclusion does not relax it. The temptation at the close of a long argument is to let the structural plausibility of the mechanism harden into an asserted result. The dissertation resists that. The mechanism that predicts H1 is well-supported by theory: three independent traditions, queueing analysis of deadline-driven waits, Forrester's system dynamics of looped and delayed feedback, and Taleb's discipline of testing for rather than assuming fat tails, converge on the same prediction. That convergence justifies treating H1 as the hypothesis worth the cost of a dissertation-scale test. It does not justify treating H1 as established. The empirical question, whether the real logs realize the predicted shape, remains open by construction, and this chapter's job is to state precisely what is closed, what is open, and what the next investigator should do.

## 8.1 The problem this chapter addresses

The problem frame for a conclusion is narrower than the frame for the dissertation as a whole. The dissertation addressed the problem that the DSN penalty's shape is unmeasured; this chapter addresses the problem of what a reader should take away from a design that has not yet been run, and how that takeaway should be calibrated.

The current state, at the close of the work, is that the reader holds a fully specified design, a complete identification strategy, a pre-registration of estimands and decision rules, and a set of illustrative results that demonstrate the form a positive finding would take. The desired state is that the reader leaves with a correctly calibrated understanding: knowing exactly which claims are theoretical and untested, which are methodological and settled, and which are empirical and deferred, so that no part of the design is over-read as a result and no part is under-read as mere speculation. The gap between the two is the gap that every design-stage dissertation must close at its end, the gap between a plan's internal completeness and a reader's correct weighting of it. A conclusion that simply re-asserted the contribution would widen this gap, because it would invite the reader to carry the illustrative figures forward as estimates. The consequence of leaving the gap open is that the work would be either dismissed as unfalsifiable speculation or, worse, cited as having shown a concentration it has not yet tested for. This chapter closes the gap by separating, explicitly and clause by clause, the established from the open, by defending the both-outcomes-are-useful structure that makes the design worth executing, and by handing the next investigator a concrete program for execution on the full data.

## 8.2 Restatement of the falsifiable contribution and the reframing

The central move of this dissertation is a reframing. It takes a fact that the operational literature already accepts, that the Deep Space Network is structurally oversubscribed and that contention forces some requested passes to be dropped, reduced, or served late [\[10\]](#ref-10), [\[17\]](#ref-17), [\[35\]](#ref-35), [\[22\]](#ref-22), and converts it from a known average into a measurable distributional question. The reframing is the contribution's pivot, and it is worth restating why it is not trivial. An aggregate satisfaction rate, even when reported, is a mean, and a mean is silent on whether the unserved requests are scattered thinly across all missions and all calendar times or are bunched onto a small set of structural windows. The two cases are observationally identical at the level of the mean and operationally opposite at the level of remedy. This is the precise sense in which the dissertation's question is not answered by the existing literature: the scheduling-optimization tradition produces better schedules and reports their objective values [\[10\]](#ref-10), [\[11\]](#ref-11), [\[15\]](#ref-15), [\[32\]](#ref-32), [\[33\]](#ref-33), and the capacity-forecasting tradition projects aggregate loading [\[17\]](#ref-17), [\[18\]](#ref-18), but neither decomposes the residual penalty into a distribution over requests or over windows.

The falsifiable contribution, restated verbatim from the contribution the dissertation has carried throughout, is the claim about that distribution. Under H0, request-to-allocation wait times and pass-loss events are adequately described by a light-tailed distribution, no small subset of geometry, band, or phase windows accounts for a disproportionate share of lost downlink, the Gini coefficient of lost downlink across windows is low, and the top-decile window share of loss is near the ten percent that uniformity predicts. Under H1, the wait-time and pass-loss distributions exhibit heavy tails better described by a power-law, log-normal, or generalized-Pareto upper tail than by an exponential, and a minority of identifiable geometry and phase windows account for a majority of the lost downlink. The acceptance rule is conjunctive and was fixed before any estimation: the contribution is accepted only if both the wait-time-tail clause and the concentration clause pass their pre-registered tests, and either clause failing refutes it. The heavy-tail clause is adjudicated by likelihood-ratio comparison of candidate distributions against the exponential and by goodness-of-fit on the fitted tail, following the maximum-likelihood-plus-goodness-of-fit framework that is the standard implementation of the test-do-not-assume instruction [\[4\]](#ref-4), [\[5\]](#ref-5), [\[6\]](#ref-6). The concentration clause is adjudicated by whether the top-decile loss share is materially above the ten percent uniformity benchmark and by the corresponding Gini coefficient. Because each clause has a pre-registered test with a pre-registered threshold, the contribution is falsifiable in the strict sense: there is a clearly specified state of the data under which it is rejected, and that state is a live possibility, not a foil.

What makes this contribution scientific rather than rhetorical is exactly that the null is reachable. A heavy-tail study that could only confirm a fat tail, because it chose its threshold after seeing the data or compared its candidate models informally, would manufacture support from noise. The dissertation guards against this by fixing the threshold-selection diagnostics, the model-comparison test, and the small-sample concentration correction in advance, so that the eventual finding is determined by the logs and the rule rather than by analyst discretion after the fact. The reframing, then, is not merely a relabeling of a known problem; it is the construction of a test that the known problem has never been subjected to, and the contribution is that test together with the falsifiable claim it adjudicates.

## 8.3 What stands and what remains open at the design stage

It is essential to state plainly what the dissertation establishes even though it has executed no estimation, because a design-stage contribution that cannot articulate its standing assets is indistinguishable from a promissory note. Several things stand independently of how the data eventually fall.

First, the reframing itself stands. The argument that an aggregate satisfaction rate cannot distinguish a uniform penalty from a concentrated one is a logical claim about what a mean can and cannot encode, and it does not depend on the empirical shape of the DSN penalty. The mean is silent on the distribution by definition. This claim is established at high confidence because it is a property of the statistic, not a conjecture about the world.

Second, the mechanism stands as a theoretically coherent prediction, at moderate-to-high confidence as a prediction and at undetermined confidence as a fact. The dissertation named the causal chain rather than asserting a bare correlation: many missions locally optimize by submitting requests early, padding requested durations, and escalating priority for critical phases; looped and delayed feedback in Forrester's sense piles those locally optimal requests onto the same shared geometry and phase windows; and the queueing structure of the DSN, with its hard deadline-driven viewing-window closures, its bursty clustered arrivals, and its skewed service requirements, supplies three independent routes by which moderate average load is converted into a heavy upper tail of waits for the deferred subclass [\[8\]](#ref-8), [\[7\]](#ref-7), [\[9\]](#ref-9), [\[21\]](#ref-21), [\[23\]](#ref-23), [\[48\]](#ref-48), [\[50\]](#ref-50), [\[51\]](#ref-51), [\[52\]](#ref-52). The observable effects this chain predicts are a heavy-tailed wait and loss distribution, lost downlink concentrated on a minority of windows, and a convex lost-downlink-versus-load curve that is Taleb's fragility signature [\[28\]](#ref-28), [\[29\]](#ref-29). The dissertation is careful that this is a mechanism and not a correlation: each link names a driver, a mediating process, and a downstream consequence, so that if the data show concentration the design can say why, and if the data show uniformity the design can say which link of the chain failed. The standing asset is the chain, not its confirmation.

Third, the method stands. Survival analysis of right-censored time-to-event data via the Kaplan-Meier estimator and the Cox proportional-hazards model [\[2\]](#ref-2), [\[1\]](#ref-1), [\[3\]](#ref-3), heavy-tail fitting via the Clauset-Shalizi-Newman procedure and generalized-Pareto peaks-over-threshold estimation [\[4\]](#ref-4), [\[54\]](#ref-54), [\[58\]](#ref-58), and concentration measurement via the Gini coefficient and top-decile share with small-sample correction, are mature methods in their home disciplines. The dissertation's methodological contribution is their assembly and aiming at DSN scheduling logs, which has not been done before, and that assembly stands as a usable pipeline whether or not it has yet been run.

What remains open is the single thing the design exists to resolve: the empirical shape of the penalty. Whether the wait-time tail is heavy or exponential, whether the top-decile window share is near sixty percent or near ten, and whether the load-response curve is convex or linear are all undetermined until the plan is executed on the full logs. The dissertation does not know these answers and does not pretend to. This is not a weakness to be apologized for; it is the defining property of a pre-registered design, whose informativeness depends precisely on the empirical answer being unknown while the decision rule is fixed.

It is worth restating, at the close, how the argument that runs through the dissertation holds together even though no estimation has been performed, because the standing of a design-stage contribution is exactly the standing of the reasoning behind it. The argument rests on five propositions. The problem is real: the DSN is structurally oversubscribed and contention forces drops, reductions, and late service, which the operational and forecasting literature documents and does not dispute [\[10\]](#ref-10), [\[17\]](#ref-17), [\[35\]](#ref-35). The problem is material: a lost or reduced pass is lost science return and, in navigation-critical phases, lost tracking that degrades orbit determination, and the magnitude grows with mission count and per-mission data rate [\[17\]](#ref-17), [\[31\]](#ref-31), [\[34\]](#ref-34). The intervention addresses the mechanism: a distributional design built from survival analysis, heavy-tail fitting, and concentration measurement directly measures the tail and the concentration the named mechanism predicts, rather than reporting a mean that is silent on both [\[2\]](#ref-2), [\[1\]](#ref-1), [\[4\]](#ref-4). The design beats the alternative: the status-quo aggregate satisfaction rate and the optimization-only literature cannot distinguish a uniform penalty from a concentrated one, because the mean encodes neither tail nor concentration, whereas the pre-registered tests adjudicate the two cases directly [\[10\]](#ref-10), [\[11\]](#ref-11), [\[15\]](#ref-15). The residual risk is acceptable: the pre-registered decision rules, the goodness-of-fit step, the small-sample concentration correction, and the fixed-effects identification bound the false-positive risk that has historically plagued heavy-tail and concentration claims, and the null is a live, reportable outcome rather than a foil [\[4\]](#ref-4), [\[77\]](#ref-77), [\[27\]](#ref-27). Each proposition is supported at the design stage by argument and by the assembled corpus rather than by estimation, and the standing of the whole is therefore the standing of those arguments, which is high for the first, second, and fourth and moderate-to-high for the third and fifth, with the one acknowledged soft spot being the lightly cited orbit-determination consequence in the materiality proposition, flagged in Section 8.5 as the recommended evidence top-up.
The rival explanations that the discussion raised also remain answerable at the design stage, and stating their disposition here completes the open-versus-closed accounting. Three rivals threaten any eventual concentration finding. The first is that concentration could be an artifact of a few atypical missions rather than a structural property of the network; the mission fixed effects and a leave-one-mission-out robustness check are built into the design to absorb and probe this, so the rival is addressed by construction even before the data arrive. The second is that an apparent heavy tail could be an artifact of threshold choice in the tail fit; the pre-registered mean-residual-life and parameter-stability diagnostics and the goodness-of-fit step are the standard guard against this, and they are fixed in advance [\[4\]](#ref-4), [\[5\]](#ref-5), [\[58\]](#ref-58). The third is that loss concentrated on geometry windows could reflect that those windows are simply when the most valuable science is requested, so the loss is high-value by selection rather than by contention; the criticality-weighted construct and the within-mission identification separate value from contention. None of these rivals is settled by the dissertation, because settling them requires the data, but each has a pre-committed response, which is what a design owes its examiner.

## 8.4 Both outcomes are useful: the symmetry that justifies the work

A design is worth executing only if its possible outcomes are each actionable, and a recurring failure mode of empirical research is the study whose null result is treated as a non-finding to be buried. This dissertation is built on the opposite premise, and the symmetry of its two outcomes is the core of its justification.

Consider first the confirmation case. If the full-data estimation accepts both clauses, finding a heavy wait-time tail with a significantly positive generalized-Pareto shape parameter and a top-decile window share materially above the uniformity benchmark, then the penalty is concentrated and the design has localized the carrying windows. The operational implication, developed in the discussion, is that the highest-return interventions are targeted rather than broad: aperture or antenna arraying deployed to the specific complexes, bands, and epochs the analysis identifies; scheduling-discipline changes that protect the systematically deferred subclass whose deferral produces the heavy tail; and demand shaping that negotiates request timing and downlink requirements so that the locally optimal padding and early submission do not pile onto the shared windows. Each lever is keyed to the carrying windows the analysis names, and each is testable by re-running the same design on post-intervention logs. Confirmation converts a known average shortfall into a localized target and tells the planner where to spend.

Consider now the refutation case, which is where the symmetry matters most. If the wait-time tail is statistically indistinguishable from exponential, the top-decile loss share is near ten percent, and the load-response curve is linear or concave, then H0 survives and the contribution is refuted. This is not a wasted result. It establishes, on the actual logs rather than on a plausibility argument, that the penalty is uniform, which is itself a decision-relevant finding: it tells NASA that targeted interventions buy little and that only broad capacity expansion meaningfully reduces the penalty. It retires a structurally plausible conjecture that, left untested, would otherwise continue to motivate targeted spending on the supposition that the loss is concentrated. A refutation of H1 is therefore a positive contribution to capacity planning, because it redirects investment from a targeting strategy that the data show would not pay to a broad-expansion strategy that the data show is necessary. The asymmetry that Taleb's discipline warns against, the asymmetric cost of falsely assuming thin tails, is why the test is worth running in both directions: if the tail is in fact heavy and the planner assumes it is thin, the exploration-era exposure is badly understated, and only a test that can find the heavy tail protects against that error (the precautionary-principle and convex-response arguments). The design's value does not ride on H1. It rides on the fact that the logs can adjudicate H0 against H1 at all, which the existing aggregate-satisfaction-rate practice cannot.

## 8.5 Decision relevance for NORTH STAR navigation and guidance planning

The dissertation sits in the navigation and guidance category, and the conclusion should make explicit why a study framed as a queueing-and-survival analysis of a communications schedule is a navigation contribution and not merely a communications one. The connection runs through the dual function of a DSN tracking pass. A pass is simultaneously a downlink opportunity, carrying science and engineering telemetry, and a radiometric tracking opportunity, generating the Doppler and range observables from which orbit determination is computed. When contention causes a pass to be dropped, reduced, or served late, the mission loses not only data return but also tracking, and lost tracking in a navigation-critical phase degrades orbit-determination accuracy at exactly the moments, maneuvers, encounters, and entry-descent-and-landing windows, when accuracy matters most. The penalty the dissertation characterizes is therefore a navigation penalty as much as a science-throughput one, and the mission-phase covariate in the design, which distinguishes critical phases from cruise, is the variable that carries this navigation stake into the estimation.

The decision relevance for portfolio-level navigation and guidance planning is concrete. If the penalty is concentrated on critical-phase windows, then the windows that carry the lost downlink are disproportionately the windows that carry degraded navigation, and the targeted-intervention case acquires a second justification beyond science return: protecting those windows protects orbit-determination accuracy for the missions in their most demanding phases. A planner allocating constrained aperture across a portfolio would, under a concentration finding, have a data-grounded basis for prioritizing critical-phase tracking at the carrying complexes and epochs rather than spreading protection uniformly. The dissertation does not assert that this prioritization is warranted; it builds the design that would tell a planner whether it is. The honest qualification, flagged at the design stage, is that the corpus is comms-and-scheduling-heavy and that the orbit-determination-degradation link, while operationally well-understood, is lightly cited in the assembled references; strengthening the navigation stake with one or two radiometric-tracking orbit-determination-accuracy sources is a recommended top-up before the navigation framing is leaned on in any execution of the design. The claim here is stated at moderate confidence as a consequence of the dual function of a pass, and the evidence that would raise it is a quantified mapping from lost tracking passes to orbit-determination covariance growth in the specific mission phases the design isolates.

## 8.6 Future research: the path to executing the design on the full data

The most important future-work item is the obvious one: execute the design. The dissertation has specified a pipeline; the next investigator should run it. This subsection lays out a concrete program for doing so, in the order the dependencies require, so that the path from this design-stage plan to a tested finding is not left as an aspiration but as a sequence of defined tasks.

The first task is data assembly and access. The design names three data sources, the DSN scheduling and tracking logs available through the service catalog and the Service Preparation Subsystem schedule archives, the NTRS DSN loading and forecasting reports, and the mission downlink-requirement records held in mission service agreements [\[10\]](#ref-10), [\[16\]](#ref-16), [\[17\]](#ref-17). The least-sourced and most access-dependent of these is the mission downlink-requirement and criticality-weight record, which no public citation fully documents and which must be obtained through mission service agreements. The execution program should therefore begin by securing the data-use arrangements for the raw scheduling logs and by negotiating access to the downlink-requirement records, because the criticality-weighted construct that the construct-validity robustness depends on is feasible only to the degree those records are available. Where direct log access is constrained for some intervals, the published loading reports provide aggregate cross-checks sufficient to calibrate the load covariate, and time-to-event panels can be partially reconstructed from reported summaries; but the strength of the eventual claim scales with the completeness of the raw-log access, and securing that access is the rate-limiting step.

The second task is to run the five pre-registered estimation steps in their fixed order: assemble the request-level panel joining logs to requirement records and derived geometry covariates; estimate the wait-time distribution and its tail with the Kaplan-Meier survival curve and the candidate-distribution fits; estimate the concentration of lost downlink across geometry-phase windows with the Gini coefficient and the top-decile share; estimate the conditional drivers with the Cox, logistic, and skewed-generalized-linear-model specifications under mission and epoch fixed effects; and estimate the load-response curve to test for the convexity that is the fragility signature. The decision rules are already fixed, so this step produces a verdict, not a discretionary interpretation. The investigator's discipline here is to honor the pre-registration, reporting the null cleanly if the null survives.

The third task is the post-intervention re-run. If the first execution finds concentration and a targeted intervention is subsequently deployed, capacity at a carrying complex, a scheduling-discipline change protecting the deferred subclass, or a demand-shaping negotiation, then re-running the identical design on the post-intervention logs tests whether the intervention actually relieved the carrying windows. This converts the design from a one-time characterization into an evaluation instrument, and it is the most direct way to move from describing the penalty to causally attributing changes in it, which the cross-sectional design alone cannot do.

The fourth task is the exploration-era extension. The crewed-exploration era will shift the mission mix toward high-rate, time-critical traffic and is projected to raise loading substantially [\[17\]](#ref-17), [\[18\]](#ref-18). The design cannot observe this future mix in advance, but the load-response curve it estimates is the externally valid object for extrapolation: rather than a single satisfaction rate, it predicts how the penalty scales as load rises, and a convex curve would imply that the exploration-era penalty is worse than a linear extrapolation of today's average loss. Future work should re-estimate the load-response curve as exploration-era traffic accrues, both to validate the extrapolation and to update capacity planning against the realized rather than the projected mix. A parallel supply-side extension is to fold in the alternative-aperture levers that the discussion identified, deep-space optical communications and antenna arraying, as supply expansions whose effect on the penalty's shape can be evaluated with the same instrument once they are operational (the deep-space optical communications technology-demonstration status, the ground-laser-receiver and relay-demonstration work, and the arraying background).

The fifth task is the deepening of the science-value construct. The dissertation measures lost downlink in bit-volume units and, where mission records permit, weights it by mission-declared criticality, but it acknowledges that not all bits carry equal scientific value and that a navigation-critical tracking pass has a value not captured by data volume. Future work should develop a more principled criticality weighting, ideally validated against mission-declared science priorities and against the orbit-determination-accuracy consequence discussed above, so that the concentration measured in physical units can be translated into concentration in science value, which is the quantity a planner ultimately cares about. This is also the natural place to incorporate the radiometric-tracking orbit-determination sources whose absence the design flagged, closing the one evidence gap that most limits the navigation framing.

## 8.7 Closing

The Deep Space Network is oversubscribed, and everyone who plans against it already knows this. The dissertation's wager is that what they do not yet know, and what the aggregate satisfaction rate they currently rely on cannot tell them, is the shape of the resulting penalty: whether the lost science return is smeared evenly across the calendar or piled onto a minority of orbital-geometry and mission-phase windows where many missions' local optimizations collide under delayed feedback and deadline-driven loss. The dissertation does not answer that question. It is honest, on every page, that no log has been analyzed and that every number in it is an illustrative placeholder. What it does is build the apparatus that can answer the question, fix the decision rule before the data are seen so that the answer is the data's and not the analyst's, and show that the answer is worth having whichever way it falls. If the penalty is concentrated, the work points constrained aperture, scheduling policy, and demand negotiation at the windows that carry the load, and protects the critical-phase tracking on which orbit determination depends. If the penalty is uniform, the work retires a plausible conjecture and tells NASA to expand broadly rather than target narrowly. The contribution is the reframing and the test, not a result; the confidence posture is that the mechanism is well-theorized and the empirical answer is deliberately left open; and the path forward is concrete, beginning with the data-use arrangements that would let the next investigator run the plan exactly as written. The penalty's shape, not merely its average, is thereby made into a quantity that can be measured, and that is what a design-stage dissertation is for. A network built and tended by many hands, in the service of missions that reach farther than any one of them could alone, deserves to be planned against its true load and not a comforting average; to set that measurement within reach, and to leave the verdict honestly to the data, is the modest service this work hopes to render.
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# Appendices

This back matter serves the reader who must check the dissertation's evidentiary chain and reproduce its design, and it does so in two parts: a single-style reference list that renders every source the argument leans on with a clickable digital object identifier, and a set of appendices that fix the operational definitions, derivations, instrument details, and supplementary tables a replication would need. The appendices are not decoration. They are the place where the design-stage commitments of this dissertation are pinned down precisely enough that a later analyst, working the actual Deep Space Network (DSN) scheduling logs, could execute the plan exactly as proposed, or could show that a specific construct was mis-specified. Because this is a design-stage analysis plan and not an executed study, the appendices carry a particular burden: they must make the pre-registered choices auditable before any data touch the estimators, since pre-registration that cannot be inspected is not pre-registration at all. Every numerical value that appears in the appendices is an illustrative placeholder describing the form a result would take, never a computed finding, and is labeled as such wherever it appears.

## Appendix A. Variable and Data Dictionary

The dictionary fixes the constructs defined in Chapter 1, so that the same symbol means the same thing in the survival model, the heavy-tail fit, and the concentration metric. The primary unit of analysis is the tracking-pass request: one requested activity, for one mission, on one antenna class, over one viewing window. The secondary unit is the geometry-phase window: a discretized cell formed by the cross of an orbital-geometry condition, a mission phase, a complex, and a frequency band, over which lost downlink is aggregated to test concentration. Holding these two units distinct matters because the wait-time and pass-loss claims live at the request level while the concentration claim lives at the window level, and conflating them would let a window-level concentration result masquerade as a request-level one.

The dependent constructs are three. Wait time, denoted \(W_i\) for request \(i\), is the elapsed time from request submission to confirmed allocation; it is right-censored, with indicator \(c_i\), for requests still pending at the observation cutoff and for requests whose viewing window expires before service. Censoring is not a nuisance here but a substantive feature: a request whose window closes unserved is a deadline-driven loss, the queueing analogue of customer abandonment, and the survival machinery of Kaplan and Meier [\[2\]](#ref-2) and Cox [\[1\]](#ref-1) exists precisely to use such incomplete observations rather than discard them. The pass-loss indicator \(L_i\) is binary, set to one when a requested pass is dropped, expires, or is reduced below a science-useful threshold, and zero when the pass executes as requested. The lost-downlink magnitude \(D\) is the shortfall between requested and executed data return for a lost or reduced pass, expressed in physical bit-volume units, and optionally weighted by mission-declared criticality; aggregated to a window it is written \(D_w\). The criticality weight is the construct most exposed to the access limitation flagged in the data chapter, because per-mission critical-event windows are documented in mission service agreements rather than in any public artifact, so the weighted variant of \(D\) is treated as a robustness check rather than as the primary dependent variable.

The covariate vector \(X\) carries four families. Orbital-geometry covariates include target declination, viewing-window overlap among concurrently supported targets, the elevation profile at each complex, and any conjunction or occultation condition that compresses the usable window; these are the variables that the celestial mechanics of a target's trajectory set independently of any mission's scheduling behavior, which is why the design treats geometry-driven window compression as a behavior-free robustness instrument. Frequency band is the requested band (for example S, X, or Ka), which governs antenna eligibility and contention with other band users, a dependence the radio-astronomy and demand-access descriptions of the network make explicit [\[34\]](#ref-34), [\[35\]](#ref-35). Concurrent-mission load is the count and the aggregate requested antenna-time of competing missions on the same complex and band in the same interval; this is the realized covariate that operationalizes the system-dynamics inflow-shape variable, the timing of the inflow rather than its total. Mission-phase is a categorical indicator separating critical phases (launch, maneuver, encounter, entry-descent-landing) from cruise. Two fixed-effect families absorb confounders: mission fixed effects \(\mu_m\) remove time-invariant mission characteristics such as instrument data rate, priority class, and strategic-padding behavior, and epoch fixed effects \(\lambda_t\) remove network-wide shocks such as an antenna in maintenance or a portfolio-wide surge.

A recurring caution belongs in the dictionary rather than buried in prose: requested time is a hedged quantity, not a clean demand signal. Missions submit early and pad requested durations to protect themselves against being cut, so the requested-time field overstates true need by an unknown, behavior-driven margin. The dictionary therefore records requested time as an observed but endogenous field, and the identification strategy, not the measurement, is what is asked to carry the weight of separating contention from intention.

The geometry-phase window deserves an explicit construction rule, because the concentration result is sensitive to how the cell is drawn. A window is defined by binning each of its four constituent dimensions and taking the cross-product of the bins. Orbital geometry is binned by declination band and by a viewing-window-overlap index that counts how many concurrently supported targets share a usable elevation window at the same complex during the interval; mission phase enters as the categorical critical-versus-cruise indicator; complex is the three-way Goldstone, Madrid, or Canberra factor; and band is the S, X, or Ka factor. The bin widths are themselves a modeling choice, and the dictionary fixes the default while requiring a sensitivity sweep, because too coarse a binning can manufacture apparent concentration by lumping many requests into a few large cells, while too fine a binning can dissolve real concentration into noise. The Gini and top-decile statistics are therefore reported across a grid of binning resolutions, and a concentration claim is credited only if it survives that grid rather than appearing at a single convenient resolution. This discipline is the dictionary-level guard against the threshold-and-binning artifact that the discussion chapter names as a rival explanation, and it is the reason the window construction is documented here at the level of the bin rather than left to the estimation step.

## Appendix B. Derivations and Estimator Specifications

This appendix records the three estimator forms so that the analysis plan is reproducible without re-deriving them. The survival layer rests on the relationships among the survivor function \(S(t)\), the density, and the hazard, which are linked one-to-one in a single-risk setting: the hazard is the instantaneous rate of allocation given survival to time \(t\), and the survivor function is the exponential of the negative integrated hazard. The Kaplan-Meier estimator [\[2\]](#ref-2) gives the nonparametric survivor function of the wait as a product over observed allocation times of one minus the ratio of allocations to the at-risk set, which handles censoring without a distributional assumption. The Cox proportional-hazards model [\[1\]](#ref-1) writes the allocation hazard as \(h(t \mid X) = h_0(t)\exp(\beta'X)\), where the baseline hazard \(h_0(t)\) is left unspecified and the covariate effects enter multiplicatively through the partial likelihood; covariates that lower the allocation hazard lengthen the wait, which is the inverse-intuition the interpretation must keep straight. Because concurrent load changes while a request waits, the design admits time-varying covariates through the counting-process extension of the Cox model [\[3\]](#ref-3), and because a request can exit to either allocation or expiry, the competing-risks caution applies: the naive Kaplan-Meier that treats the competing exit as ordinary censoring is biased, and the cause-specific hazard must be modeled separately [\[64\]](#ref-64). Where raw event times are inaccessible for some interval and only summary survivor curves are reported, the published-curve reconstruction algorithm permits an approximate individual-level panel to be rebuilt from digitized survivor curves and at-risk counts [\[88\]](#ref-88), a fallback the data chapter relies on rather than abandoning the affected interval.

The heavy-tail layer fixes the families and the decision procedure. The empirical wait-time and lost-downlink distributions are fit to four candidates: the exponential, which is the light-tailed null benchmark; the log-normal; the power-law, with exponent \(\alpha\); and the generalized Pareto for the upper tail, with scale \(\sigma\) and shape \(\xi\). The formal heavy-tail signature is a significantly positive shape \(\xi\), since a positive shape gives a Pareto-type tail with polynomially decaying survivor function. The fitting follows the Clauset-Shalizi-Newman maximum-likelihood-plus-goodness-of-fit procedure [\[4\]](#ref-4), which estimates the lower bound of power-law behavior, fits by maximum likelihood above it, and assesses fit by a semiparametric bootstrap rather than by a naive coefficient of determination on log-log axes; the implementations are the powerlaw [\[5\]](#ref-5) and poweRlaw [\[6\]](#ref-6) packages. Non-nested candidates are compared by likelihood-ratio test, and the upper tail is additionally estimated by peaks-over-threshold with a generalized Pareto fit, the standard extreme-value estimator above a high threshold [\[54\]](#ref-54), [\[58\]](#ref-58), with the threshold chosen by mean-residual-life and parameter-stability diagnostics rather than post hoc. The concentration layer is arithmetic but must be specified to avoid ambiguity: lost downlink is aggregated to geometry-phase windows, the Gini coefficient \(G\) of \(D_w\) across windows summarizes inequality [\[76\]](#ref-76), and the top-decile share \(T_{10}\) records the fraction of total loss carried by the most-affected ten percent of windows. The small-sample bias of the Gini is acknowledged explicitly, because the number of windows can be modest and the uncorrected Gini is downward-biased in small populations [\[77\]](#ref-77); the bias-adjusted estimator and a concentration-index cross-check [\[78\]](#ref-78), [\[79\]](#ref-79) are carried as robustness variants. The pass-loss regression is a logistic model in the log-odds of \(L_i\) with the full covariate vector and the two fixed-effect families, and the continuous magnitude \(D\) is modeled by a generalized linear model suited to skewed, non-negative support.

## Appendix C. Instrument, Query, and Data-Access Details

The named data are three. The DSN scheduling and tracking logs are the request, allocation, and execution records produced by the deployed scheduling system and exposed through the DSN service catalog and the Service Preparation Subsystem schedule archives; the workflow that generates them, from long-range forecasting through mid-range negotiation to near-real-time conflict resolution, is documented in the operational literature [\[10\]](#ref-10), [\[16\]](#ref-16). Each record documents the requesting mission, the requested antenna or antenna class, the requested window, the band, the activity type (telemetry, command, or radiometric tracking), the negotiated allocation if any, and the executed pass if any; the request-to-allocation-to-execution triple is exactly the time-to-event structure the survival layer consumes. The second source is the set of NASA Technical Reports Server (NTRS) loading and forecasting reports, which report aggregate oversubscription by complex, band, and epoch and which supply the validated demand context against which the log-derived load covariate is checked [\[17\]](#ref-17), [\[31\]](#ref-31). The third source is the mission downlink-requirement records, maintained in mission service agreements, which convert a lost pass into a quantified lost-downlink magnitude and identify the critical-phase windows used as covariates; this is the most access-dependent input and the one whose criticality weights may be only partially recoverable.

The access path is staged so that a constrained-access interval does not defeat the design. The NTRS reports are publicly retrievable; the scheduling and tracking logs are obtained through the service-catalog and schedule-archive interfaces under the appropriate data-use arrangements; the mission requirement records come from the service agreements. Where direct log access is constrained, the published loading reports provide aggregate cross-checks sufficient to calibrate the load covariate, and the survivor-curve reconstruction method [\[88\]](#ref-88) supplies an approximate event-level panel from reported summaries. No queries have been run against the logs; the dissertation is a plan, and this appendix specifies the retrieval and join procedure rather than reporting any retrieval result. The intended coverage is a multi-year span sufficient to include several cycles of the recurring high-contention windows and a representative set of mission phases across mission classes, because the tail of the wait and loss distributions can be fit only if it is observed often enough, which is the design-stage operationalization of the warning against short records that undersample the tail.

## Appendix D. Supplementary Tables

### Table D.1. Notation register

| Symbol | Meaning | Appears in |
|---|---|---|
| \(W_i\), \(c_i\) | wait time and censoring indicator of request \(i\) | survival layer |
| \(L_i\) | pass-loss indicator (1 = dropped/expired/reduced) | loss regression |
| \(D\), \(D_w\) | lost-downlink magnitude; aggregated to window \(w\) | concentration |
| \(S(t)\) | Kaplan-Meier survivor function of the wait | survival layer |
| `h(t \| X)` | allocation hazard, Cox \(h_0(t)\exp(\beta'X)\) | survival layer |
| \(\alpha\) | power-law exponent | tail fit |
| \(\sigma\), \(\xi\) | generalized-Pareto scale and shape; `xi > 0` = heavy tail | tail fit |
| \(G\), \(T_{10}\) | Gini of \(D_w\); top-decile window share of loss | concentration |
| \(\mu_m\), \(\lambda_t\) | mission and epoch fixed effects | identification |

### Table D.2. Estimand-to-estimator-to-decision-rule crosswalk (illustrative thresholds, not computed)

| Estimand | Estimator | Pre-registered decision rule |
|---|---|---|
| Shape of wait-time tail | KM survivor [\[2\]](#ref-2); exponential vs log-normal/power-law/GPD [\[4\]](#ref-4), [\[5\]](#ref-5), [\[6\]](#ref-6) | accept H1-wait if likelihood-ratio prefers a heavy-tailed model over exponential and GPD shape \(\xi\) is significantly positive |
| Shape and concentration of loss | Gini \(G\) and \(T_{10}\) over windows [\[76\]](#ref-76), [\[77\]](#ref-77), [\[78\]](#ref-78) | accept H1-concentration if \(T_{10}\) is materially above the 10% uniformity benchmark (illustrative pre-set threshold \(T_{10}\) >= 0.40) and \(G\) is correspondingly high |
| Conditional pass-loss drivers | Cox hazard [\[1\]](#ref-1), [\[3\]](#ref-3); logistic + skewed GLM with \(\mu_m\), \(\lambda_t\) | report covariate associations for geometry, band, load; not a clause of the contribution |
| Load-response curvature | expected \(D\) versus concurrent load [\[29\]](#ref-29) | convex (accelerating) curve is the fragility signature; linear or concave is consistent with H0 |

### Table D.3. Summary of the dissertation's argument

| Proposition | Statement | Evidencing references |
|---|---|---|
| Problem is real | DSN is structurally oversubscribed; contention forces drops and reductions | [\[10\]](#ref-10), [\[16\]](#ref-16), [\[17\]](#ref-17), [\[31\]](#ref-31), [\[33\]](#ref-33), [\[35\]](#ref-35) |
| Problem is material | Lost downlink is lost science and degraded navigation tracking, growing with mission count and data rates | [\[17\]](#ref-17), [\[22\]](#ref-22), [\[31\]](#ref-31), [\[34\]](#ref-34) |
| Intervention addresses the mechanism | A distributional queueing-plus-survival method measures the tail and concentration the mechanism predicts | [\[1\]](#ref-1), [\[2\]](#ref-2), [\[4\]](#ref-4), [\[7\]](#ref-7), [\[8\]](#ref-8), [\[9\]](#ref-9), [\[48\]](#ref-48), [\[51\]](#ref-51) |
| Beats alternatives | A mean satisfaction rate cannot distinguish uniform from concentrated; optimization-only work does not characterize the residual penalty | [\[11\]](#ref-11), [\[12\]](#ref-12), [\[13\]](#ref-13), [\[14\]](#ref-14), [\[15\]](#ref-15), [\[32\]](#ref-32), [\[33\]](#ref-33) |
| Residual risk acceptable | Pre-registered decision rules, goodness-of-fit, and fixed-effect identification bound false positives; the null is a live, reportable outcome | [\[4\]](#ref-4), [\[6\]](#ref-6), [\[27\]](#ref-27), [\[77\]](#ref-77) |

The argument reads as a single conditional: the problem is real and material, the proposed distributional design addresses the named causal mechanism rather than a bare correlation, it beats the status-quo mean by recovering the shape the mean conceals, and its residual risk is bounded by pre-registration. The confidence posture is design-stage throughout. The mechanism for the heavy-tailed-and-concentrated alternative is well-supported in theory, resting on three concurrent queueing routes to heavy tails (deadline-driven abandonment, bursty arrivals, and skewed service) together with the system-dynamics account of why locally optimizing missions pile demand onto shared windows [\[21\]](#ref-21), [\[26\]](#ref-26). Whether the alternative holds on the real logs is untested by construction, and the plan is built so that the null is falsifiable and a clean refutation, which would itself justify broad rather than targeted capacity expansion, remains a reportable result.