Testing a congestion claim: bursts, backlog and stability

INCOPREA / RESEARCH

Research notebook · October 30, 2026 · Exact model calculation

Can bursts destabilize a queue with spare capacity on average? An exact calculation helps separate backlog from instability.

We examined one mechanism proposed in Congestion Onset Is Variability, Not Volume. Our simplified queue has unlimited storage and capacity C = 1 unit of work per time slot. These are units of work, not cars. Arrivals enter before service; the queue is measured afterward.

Same average, different backlog. Constant arrivals of 0.8 units per slot leave an initially empty queue at zero. Sending four units every five slots has the same average, 0.8, but produces repeating post-service queues of 3, 2, 1, 0, 0.

For any starting queue Q ≥ 0, a complete burst period maps Q to max(0, Q − 1). The queue therefore drains rather than growing indefinitely.

This is an exact mathematical counterexample to the explanation that sufficiently bursty arrivals must destabilize an underloaded queue in this model. Bursts create waiting and larger temporary queues. Those effects are distinct from instability.

Classical queueing work makes the assumptions central: Loynes (1962) classifies stability regimes; Glynn and Zeevi (2008, §5.1) distinguish stationary behavior and mean waiting under specified random-input conditions. Our periodic result follows directly from the recurrence.

Real-road validation, finite storage, spillback and policy costs remain untested. This calculation narrows one mechanism without disproving the whole traffic hypothesis. Inspect the full report, code and data.

Prepared with Codex AI assistance from the exact queue proof and primary references. Not peer reviewed; no claim of novelty or validation on real roads.

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