Kingman's Formula
Updated 2026-08-02
INTRODUCTION
English translation pending.
CORE DEFINITION
Derived by John Kingman, the formula approximates average waiting time in a single-server queue as a function of utilization and the variability of arrival and service times. It shows that as utilization approaches one, waiting time grows roughly in proportion to one divided by one minus utilization, so it diverges rather than rising gently. The practical qualification is that the result applies to a single server with general arrival and service distributions, and that both high utilization and high variability drive the blow-up.
SCAFFOLDING EFFECT
Reduce cognitive load
- Justify the slack: treat spare capacity as a mathematical requirement rather than wasted resources. - Watch variability: reduce the spread of arrival and service times, not only the average load. - Predict the cliff: expect delay to rise sharply once utilization passes a safe threshold.
Anchor fast decisions
The formula separates delay into three parts: a utilization term that grows as one divided by one minus utilization, a variability term driven by the squared coefficients of variation of arrivals and service, and a service-time factor. Because the utilization term diverges near full load, small random fluctuations can no longer be absorbed by spare capacity. That is why a system running near its limit degrades abruptly rather than gradually, and why reserving slack preserves flow.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Kingman's_formulaverified
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