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The build‐up time of waiting lines

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  • Harold Davis

Abstract

This paper is concerned with the transient build‐up to steady‐state of a simple queue system (Poisson arrivals with constant mean rate, exponential service times with common means, constant number of available channels, etc.). As a substitute for the tracing out of the detailed buildup to the steady‐state, a nominal indicator of the time required to reach the steady‐state is introduced. The dependence of this nominal build‐up time on the system parameters (traffic intensity, steady‐state mean, etc. ) is shown. In particular, if there are s service channels, and if m1, the mean number in the system at steady‐state, is reasonably large, then this nominal build‐up time is approximately equal to m12 /s mean service periods. In some applications, this can exceed the duration of existence of the queue discipline, thus vitiating the use of steady‐state probabilities.

Suggested Citation

  • Harold Davis, 1960. "The build‐up time of waiting lines," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 7(2), pages 185-193, June.
    • Handle: RePEc:wly:navlog:v:7:y:1960:i:2:p:185-193
    DOI: 10.1002/nav.3800070207
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