--- marp: true theme: default paginate: true --- # Deep Space Network as a Queue ### Contention, Wait-Time, and the Science-Throughput Penalty of Antenna Scheduling **Dissertation defense** **Candidate:** JPL_INSTRUMENTS_NAV_05 **COLLEGIUM 1st Battalion** **Category:** Navigation and Guidance **Stage:** Design-stage analysis plan (no logs analyzed; all magnitudes illustrative) **Date:** 2026-06-15 --- ## The Answer First: The Contribution A single falsifiable claim about the *shape* of the DSN science-throughput penalty. - **H0 (null):** Scheduling friction is roughly uniform. Request-to-allocation wait times and pass-loss events are light-tailed, and no small set of geometry, band, or phase windows carries a disproportionate share of lost downlink (top-decile share near 10%, low Gini). - **H1 (alternative):** Friction is heavy-tailed and concentrated. A minority of orbital-geometry and mission-phase windows accounts for a majority of lost downlink. Accepted only if **both** the heavy-tail clause **and** the concentration clause pass pre-registered tests. Either failing refutes it. --- ## Why It Matters: The Decision The shape, not the average, decides where NASA and JPL should spend. - If **concentrated**: targeted aperture, scheduling-policy, and demand-shaping at the carrying windows recover the most science return per dollar. - If **uniform**: only broad capacity expansion helps; the aggregate satisfaction rate is then an adequate summary. - Navigation stake: a lost tracking pass in a critical phase degrades orbit determination exactly when it matters. Concentration on critical-phase windows would fall on the most consequential passes. Either outcome is a usable planning input. Neither is a colloquial null. --- ## The Problem Frame - The DSN is a fixed set of large antennas at three complexes (Goldstone, Madrid, Canberra), shared by nearly every deep-space mission. - Supply is vertical on any planning horizon. Demand grows on three axes: more spacecraft, more data per mission, and crewed-exploration traffic ahead. - In recurring windows, requested antenna time exceeds available antenna time. The schedule must drop, shorten, or defer requests. - The residual penalty is real and acknowledged, but reported only as a **mean** (a satisfaction rate). A mean cannot tell uniform from concentrated. --- ## The Gap in the Literature Three postures, one empty cell. - **Optimization** (constraint satisfaction, MILP, evolutionary, RL, quantum annealing) is strong on mechanism, reports schedule-quality means [\[10\]](#ref-10), [\[11\]](#ref-11), [\[15\]](#ref-15), [\[32\]](#ref-32), [\[33\]](#ref-33). - **Capacity forecasting** is strong on aggregate loading and demand projection [\[17\]](#ref-17), [\[18\]](#ref-18), [\[31\]](#ref-31). - **Methodology** (queueing-tail theory, survival analysis, heavy-tail and concentration estimation) supplies the estimators but has never been aimed at scheduling loss. **Gap:** no published treatment fits the realized wait-time or lost-downlink distribution, tests its tail, or measures its concentration, for the DSN or for contact scheduling generally. --- ## Theoretical Framework: Queueing Queues do not generally produce light-tailed waits; structure, not mean load, drives the tail. - DSN maps exactly: requests are arrivals, antennas are servers, the viewing window is a hard deadline, a request past its window is lost (abandonment). - Three concurrent routes to a heavy tail, all present by construction: 1. **Deadline-driven abandonment** (hard viewing-window close) [\[48\]](#ref-48), [\[49\]](#ref-49). 2. **Bursty, clustered, self-similar arrivals** (geometry windows) [\[51\]](#ref-51), [\[52\]](#ref-52). 3. **Skewed service** (critical-event passes far longer than cruise) [\[81\]](#ref-81), [\[59\]](#ref-59). - A negotiated priority discipline systematically defers a subclass whose waits dominate the tail [\[9\]](#ref-9), [\[44\]](#ref-44). --- ## Theoretical Framework: Forrester System dynamics explains *why* concentration is structurally plausible. - State lives in **stocks**: backlog of unserved requests, accumulated unmet downlink requirement. - Stocks change through **flows**: request arrivals, pass allocations. - Coupled by **delayed feedback**: missions submit early, pad durations, escalate priority. Each is locally rational. - In aggregate, locally optimal behavior piles requests onto the same shared windows, and the relieving feedback is slower than the window. Loop structure and delay dominate, not intentions [\[21\]](#ref-21), [\[23\]](#ref-23), [\[63\]](#ref-63). --- ## Theoretical Framework: Taleb Fat-tail discipline supplies the test and the risk reading. - **Mediocristan vs Extremistan:** is the mean a fair summary, or do a few extreme windows dominate while the record undersamples the tail? - **Do not assume light tails.** Test for them; prefer the heavier model unless rejected. Thin-tail error is asymmetrically costly [\[27\]](#ref-27). - **Characterize the convex load-response** (the second-order response to load), not a forecast of the next bad window. A convex curve is the fragility signature [\[28\]](#ref-28), [\[29\]](#ref-29). --- ## The Named Causal Mechanism A chain, not a correlation. - **Driver:** missions locally optimize (submit early, pad, escalate). - **Mechanism:** delayed feedback piles requests onto shared windows; deadline geometry, bursty arrivals, and skewed service convert moderate load into a heavy tail for the deferred subclass. - **Observable effect:** heavy-tailed waits and losses; concentrated lost downlink; convex load-response. - **Operational consequence:** a few windows carry a majority of lost science and degraded tracking. - **Strategic implication:** targeted intervention recovers the most per dollar; the exploration-era penalty scales worse than linearly. --- ## Data: Three Named, Real Sources 1. **DSN scheduling and tracking logs** via the service catalog and Service Preparation Subsystem archives: request, allocation, and execution records, one per tracking-pass request [\[10\]](#ref-10), [\[16\]](#ref-16). 2. **NTRS DSN loading and forecasting reports**: aggregate oversubscription by complex, band, and epoch, the validated cross-check [\[17\]](#ref-17), [\[31\]](#ref-31). 3. **Mission downlink-requirement records** (service agreements): convert a lost pass into quantified lost downlink and define critical-phase windows. **Unit of analysis:** the tracking-pass request. **Secondary unit:** the geometry-phase window. --- ## Data: The Measurement Discipline - **Requested time is a hedged quantity, not clean demand.** Missions pad and submit early; the apparatus treats the request as a strategic artifact. - Constructs: wait `W` (right-censored), pass-loss `L` (threshold-parameterized), lost downlink `D` (bit-volume, optionally criticality-weighted), covariates `X` (geometry, band, concurrent load, phase). - Geometry covariates are set by celestial mechanics, behavior-independent, and serve as a robustness instrument. - Multi-year coverage is mandatory so the tail and carrying windows are observed often enough to fit. --- ## Design and Identification Three estimands, three matched estimators, one firewall. - **Wait-time shape:** Kaplan-Meier and Cox PH with time-varying load; competing-risks for allocation-vs-expiry [\[1\]](#ref-1), [\[2\]](#ref-2), [\[3\]](#ref-3), [\[64\]](#ref-64). - **Concentration:** Gini `G` and top-decile share `T10` over windows, **descriptive, needs no exogeneity** [\[76\]](#ref-76), [\[77\]](#ref-77), [\[78\]](#ref-78). - **Conditional drivers:** logistic and skewed GLM with mission FE `mu_m` and epoch FE `lambda_t`. - **Identification firewall:** the descriptive estimands stand on the log; only the driver regression carries an exogeneity assumption, relieved by the behavior-free geometry-compression lever. --- ## Analysis Plan: Five Pre-Registered Steps 1. Assemble the request-level panel (wait, censoring, loss, lost downlink, covariates). 2. Estimate the wait-time distribution; fit exponential vs log-normal vs power-law vs generalized Pareto (Clauset-Shalizi-Newman + peaks-over-threshold) [\[4\]](#ref-4), [\[5\]](#ref-5), [\[6\]](#ref-6), [\[54\]](#ref-54). 3. Aggregate lost downlink to windows; compute `G` and `T10`. 4. Fit Cox, logistic, and GLM driver models under fixed effects. 5. Estimate the load-response curve; test for convexity. An illustrative queueing simulation validates that the pipeline retains the null at the light-tailed corner and recovers a heavy tail when one is present. --- ## Methodological Contribution and Novelty The methods are mature in their home fields; the contribution is their assembly and their first aiming at scheduling loss. - Survival analysis of censored time-to-allocation: standard in biostatistics, never applied to allocation waits. - Clauset-Shalizi-Newman heavy-tail fitting and generalized-Pareto peaks-over-threshold: standard in physics and extreme-value statistics, never applied to scheduling-loss tails. - Gini and top-decile concentration: standard in econometrics and epidemiology, never applied to ground-station scheduling. - The transfer of queueing heavy-tail mechanisms to the DSN viewing-window deadline is a transfer-of-mechanism argument, made by construction and flagged for the examiner. --- ## Threats to Validity - **Internal:** requested time is endogenous to expected contention. Addressed by mission and epoch fixed effects plus the geometry-driven robustness lever; residual endogeneity downgrades driver-estimand confidence to moderate. - **External:** result conditioned on the studied mission mix. Report the load-response curve, not a single rate. - **Construct:** lost downlink proxies lost science. Report data-volume and criticality-weighted versions. - **Statistical-conclusion:** heavy-tail false positives controlled by pre-registered thresholds, goodness-of-fit, and small-sample Gini correction. --- ## Expected Results (Illustrative, Design-Stage, NOT Computed) **Nothing has been run on the logs. Every magnitude below is an illustrative placeholder showing the form of a positive result.** - Wait-time tail declines slowly; generalized-Pareto shape `xi` illustratively ~0.3 to 0.5; heavy-tail model preferred over exponential. - Lost downlink concentrates: illustrative `T10` ~one-half to two-thirds, against 10% under uniformity, elevated Gini. - Higher loss in conjunction-overlap windows, the most contested band, and the top load quartile. - Convex load-response: loss rises faster than linearly with load. --- ## The Symmetric Negative Result The null is a live, reportable outcome, specified with equal precision. - If the wait tail is indistinguishable from exponential, `xi` is indistinguishable from zero, `T10` sits near 10%, and the load-response is linear or concave, then H0 survives and the contribution is refuted. - This is not a failure. It establishes uniformity on the actual logs and tells NASA to expand broadly rather than target narrowly. - A design under which the null could not surface would not be a test. --- ## Confidence and Uncertainty Posture Modality is graded to the evidence, never conflated. - **Reframing** (a mean cannot distinguish uniform from concentrated): high confidence, a property of the statistic. - **Mechanism** for H1: moderate-to-high as a prediction (three converging traditions); **undetermined** as a fact until the logs are run. - **Concentration estimand:** higher design-stage confidence (descriptive, no exogeneity). - **Driver estimand:** moderate (endogeneity relieved, not eliminated). - **Causal attribution** of concentration to the feedback loop: moderate, signature-only; the cross-sectional design tests the convex signature, not the loop itself. --- ## Summary of the Argument **The thesis:** the penalty is a distribution with a measurable shape; the falsifiable claim is heavy-tailed-and-concentrated (H1) against the uniform null (H0). | Proposition | Evidence | |---|---| | 1. Problem is real | DSN structurally oversubscribed [\[10\]](#ref-10), [\[16\]](#ref-16), [\[31\]](#ref-31), [\[33\]](#ref-33), [\[35\]](#ref-35) | | 2. Problem is material | Lost downlink = lost science + degraded tracking [\[17\]](#ref-17), [\[31\]](#ref-31), [\[34\]](#ref-34) | | 3. Addresses the mechanism | Queueing+survival+heavy-tail measures tail and concentration [\[1\]](#ref-1), [\[2\]](#ref-2), [\[4\]](#ref-4), [\[9\]](#ref-9), [\[48\]](#ref-48) | | 4. Beats alternatives | A mean cannot distinguish uniform from concentrated [\[11\]](#ref-11), [\[32\]](#ref-32), [\[33\]](#ref-33) | | 5. Residual risk acceptable | Pre-registered rules, goodness-of-fit, FE; null is live [\[4\]](#ref-4), [\[6\]](#ref-6), [\[27\]](#ref-27), [\[77\]](#ref-77) | **Residual risk:** empirical realization untested by design; false-positive risk bounded by pre-registration; causal claim held to the convex signature. The study characterizes the shape of an existing capability's penalty; it specifies no new system, so an architecture-traceability layer is out of scope. --- ## Path to Execution and Future Work The design specifies a pipeline; the next investigator runs it. - Secure data-use arrangements for the raw scheduling logs and access to mission downlink-requirement records (the rate-limiting step). - Run the five pre-registered estimation steps in fixed order; honor the pre-registration and report the null cleanly if it survives. - Re-run on post-intervention logs to convert characterization into an evaluation instrument. - Re-estimate the load-response curve as exploration-era traffic accrues; fold in optical comms and arraying as supply levers. - Deepen the science-value construct and add radiometric-tracking orbit-determination sources (the one flagged evidence gap). --- ## Contribution Restated - Converts a known fact (the DSN is oversubscribed) into a measured distributional question with a single falsifiable answer. - Reframes the residual penalty from a mean into a shape: tail behavior plus concentration. - Supplies a pre-registered queueing-and-survival design that adjudicates H0 against H1 on the realized logs, with decision rules fixed before the data are seen. - Decision-relevant whichever way the data fall, and the load-response curve, not the average, is the externally valid object for the crewed-exploration era. --- ## Defense Questions Anticipated - Why are heavy tails the right null to test against, not the default assumption? - How do you separate high-value-by-selection from high-loss-by-contention? - What protects the tail fit from threshold-mining? - Can the within-mission identification hold load exogenous to a specific pass's value? - What single result on the full data would make you abandon the contribution? - Why is an architecture-traceability layer out of scope here? --- ## References (selected; full list of 96 in the dissertation) - [\[4\]](#ref-4) Clauset, Shalizi, Newman (2009). Power-Law Distributions in Empirical Data. *SIAM Review*. doi: [10.1184/r1/6586835.v1](https://doi.org/10.1184/r1/6586835.v1) - [\[9\]](#ref-9) Terekhov et al. (2014). Integrating Queueing Theory and Scheduling. *JAIR*. doi: [10.1613/jair.4278](https://doi.org/10.1613/jair.4278) - [\[10\]](#ref-10) Johnston et al. (2014). Automated Scheduling for NASA's DSN. *AI Magazine*. doi: [10.1609/aimag.v35i4.2552](https://doi.org/10.1609/aimag.v35i4.2552) - [\[21\]](#ref-21) Forrester (1961). Industrial Dynamics. *System Dynamics Review*. doi: [10.1002/sdr.284](https://doi.org/10.1002/sdr.284) - [\[27\]](#ref-27) Taleb et al. (2014). The Precautionary Principle. *arXiv*. doi: [10.48550/arxiv.1410.5787](https://doi.org/10.48550/arxiv.1410.5787) - [\[31\]](#ref-31) Abraham et al. (2025). Future Deep Space Mission Communications Trends. *Space Operations*. doi: [10.1007/978-3-031-60408-9_17](https://doi.org/10.1007/978-3-031-60408-9_17) - [\[54\]](#ref-54) McNeil (1997). Estimating the Tails of Loss Severity Distributions. *ASTIN Bulletin*. doi: [10.2143/ast.27.1.563210](https://doi.org/10.2143/ast.27.1.563210) - [\[76\]](#ref-76) Farris (2010). The Gini Index and Measures of Inequality. *Amer. Math. Monthly*. doi: [10.4169/000298910x523344](https://doi.org/10.4169/000298910x523344) A network built and tended by many hands deserves to be planned against its true load, not a comforting average. Setting that measurement within reach, and leaving the verdict to the data, is the service this work hopes to render. **Thank you. Questions welcome.**