{
  "study": "Fixed-capacity point-queue test of the variability instability claim",
  "version": "1.0",
  "committed_before_execution_utc": "2026-10-30T16:31:08.992077+00:00",
  "source_file": "/Users/tobymikle/Desktop/Original Theories Vol IV - 2026-10-30/theories/congestion-is-variability.html",
  "source_sha256": "bf91d67c48acf43df1f67fb7133c13fa84772f0490b125fd21e0fc344ae35b61",
  "source_public_url": "https://incoprea.com/research-library/original-theories-vol4-20261030/theories/congestion-is-variability.html",
  "publication_target": "https://incoprea.com/research-library/tests/congestion-20261030/",
  "scope": "Narrow mathematical/computational model check, not empirical road traffic, clinical evidence, or proof of a novel scientific theory.",
  "queue": {
    "recurrence": "Q[t+1] = max(0, Q[t] + A[t] - C)",
    "capacity_per_cycle": 1,
    "initial_queue": 0,
    "observation": "Backlog immediately after same-cycle service, not before-service workload or individual travel delay.",
    "assumptions": [
      "single infinite-storage point queue",
      "fixed service capacity",
      "arrivals applied before service",
      "no spillback, capacity drop, route choice or network blocking"
    ]
  },
  "deterministic": {
    "cycles": 100,
    "constant_arrival": "4/5 work units each cycle (fluid comparison)",
    "burst_arrival_pattern": [
      4,
      0,
      0,
      0,
      0
    ],
    "exact_arithmetic": "fractions.Fraction",
    "primary_contrast": "Matched mean4/5 and capacity1. Derive five-cycle burst map max(0,Q-1); compare bounded backlog, maximum, average and period endpoints.",
    "period_map_initial_queues": [
      0,
      1,
      10,
      100
    ]
  },
  "stochastic": {
    "arrival_family": "A[t]=b with probability rho/b, else0; independent draws within each run",
    "rho_values": [
      "0.50",
      "0.80",
      "0.95",
      "1.05"
    ],
    "batch_sizes": [
      1,
      2,
      4,
      8
    ],
    "infeasible_cell": {
      "rho": "1.05",
      "batch": 1,
      "reason": "rho/b=1.05>1; do not clip or simulate this cell"
    },
    "valid_conditions": 15,
    "replicates_per_condition": 64,
    "cycles_per_replicate": 100000,
    "burn_in_cycles": 20000,
    "measurement_cycles": 80000,
    "checkpoint_every_cycles": 5000,
    "seed_algorithm": "first8 SHA-256 bytes of UTF-8 congestion-v1|rho=<two decimal rho>|batch=<b>|replicate=<0-based index>, interpreted unsigned big-endian",
    "random_generator": "Python random.Random, a separate seeded instance per replicate and condition",
    "retained_outputs": [
      "every replicate metric and seed",
      "all run checkpoints at0 and each5000 cycles",
      "condition summary CSV/JSON",
      "exact deterministic traces and period-map table"
    ],
    "not_retained": "Individual per-cycle random arrivals/backlogs; reproducible from saved seed and code.",
    "metrics": [
      "mean post-service backlog over t=20001..100000",
      "fraction of measurement cycles Q>=10",
      "fraction of measurement cycles Q>=100",
      "fraction of measurement cycles Q=0",
      "mean arrivals over measurement window",
      "maximum measurement-window backlog",
      "Q(50000)",
      "Q(100000)",
      "late_endpoint_growth=(Q(100000)-Q(50000))/50000",
      "mean Q over t=20001..60000 and t=60001..100000",
      "half_window_growth=(late_half_mean_Q-early_half_mean_Q)/40000"
    ],
    "uncertainty": "Across64 independent seeded replicate estimates: mean \u00b12*sample_standard_deviation/sqrt(64), labelled approximate95% Monte Carlo intervals. No time-cycle IID assumption. Probability interval endpoints clipped to[0,1]; nonnegative metric endpoints clipped at0. Growth intervals remain signed.",
    "analytic_benchmark": "For rho<1 in this integer batch-Bernoulli family, stationary mean after-service Q = rho*(b-1)/(2*(1-rho)), derived from first and second moment balances. Compare results without adjusting parameters or dropping runs.",
    "interpretation_rules": [
      "Do not infer infinite-horizon stability from finite simulations alone; use exact recurrence/negative-drift theory under stated assumptions.",
      "A nonzero mean backlog or threshold exceedance is not mathematical instability or physical gridlock.",
      "Overload is expected for rho>1 where valid; do not report its finite-horizon averages as stationary means.",
      "No actual road breakdown, cost-equivalent capacity intervention or predictive-superiority test is performed.",
      "No post-hoc reruns, seed selection, horizon changes or condition exclusions beyond the predefined infeasible cell."
    ]
  },
  "figures": [
    "stable mean backlog versus batch, with replicate Monte Carlo intervals and analytic benchmarks",
    "late endpoint growth versus load, by batch, with replicate Monte Carlo intervals"
  ],
  "dependencies": "Python standard library only; no installation or network access needed to run the experiment.",
  "primary_context_sources": [
    {
      "title": "Bounding Stationary Expectations of Markov Processes",
      "authors": "Peter W. Glynn and Assaf Zeevi",
      "year": 2008,
      "section": "5.1, printed page208",
      "url": "https://web.stanford.edu/~glynn/papers/2008/GZeevi08.pdf"
    },
    {
      "title": "The theory of queues with a single server",
      "author": "D. V. Lindley",
      "year": 1952,
      "doi": "10.1017/S0305004100027638",
      "url": "https://doi.org/10.1017/S0305004100027638"
    }
  ]
}