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Average delay in queues with non-stationary Poisson arrivals

Published online by Cambridge University Press:  14 July 2016

Sheldon M. Ross
Sheldon M. Ross*
Affiliation:
University of California, Berkeley
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Abstract

One of the major difficulties in attempting to apply known queueing theory results to real problems is that almost always these results assume a time-stationary Poisson arrival process, whereas in practice the actual process is almost invariably non-stationary. In this paper we consider single-server infinite-capacity queueing models in which the arrival process is a non-stationary process with an intensity function ∧(t), t ≧ 0, which is itself a random process. We suppose that the average value of the intensity function exists and is equal to some constant, call it λ, with probability 1.

We make a conjecture to the effect that ‘the closer {∧(t), t ≧ 0} is to the stationary Poisson process with rate λ ' then the smaller is the average customer delay, and then we verify the conjecture in the special case where the arrival process is an interrupted Poisson process.

Keywords

DELAYNON-STATIONARY ARRIVALSCOMPARISON WITH STATIONARY CASE
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 602 - 609
Copyright
Copyright © Applied Probability Trust 1978 

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References

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