Little: a general stationary-queue proof linking occupancy, arrivals and time in system

What changed

Little proved L=λW for consistently defined queue occupancy, arrival rate and sojourn time under finite-mean strict stationarity and an ergodic interarrival process, extending earlier heuristic and special-model uses of the relation.

Scientific scope

Little proved L=λW for consistently defined queue occupancy, arrival rate and sojourn time under finite-mean strict stationarity and an ergodic interarrival process, extending earlier heuristic and special-model uses of the relation. The identity relates long-run occupancy, arrival rate and time in system under the paper’s stationarity/existence and accounting assumptions. It is not a pointwise identity for every finite interval or a stability proof when averages do not exist. System boundaries and customer accounting must agree. Later transient and generalized formulations are separate.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

• John D. C. Little · SCIENCE: Sole original byline author and general stationary-queue proof.
• H. Newton Garber · SCIENCE: Original acknowledgment explicitly credits equation2 and its definitional implications plus proof suggestions; not a byline coauthor.

• Little: a general stationary-queue proof linking occupancy, arrivals and time in system — complete assessed article text
• INFORMS original publication metadata and abstract: A Proof for the Queuing Formula

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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