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Average Delay in Queues with Non-Stationary Poisson Arrivals

Sheldon M. Ross
Journal of Applied Probability
Vol. 15, No. 3 (Sep., 1978), pp. 602-609
DOI: 10.2307/3213122
Stable URL: http://www.jstor.org/stable/3213122
Page Count: 8
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Average Delay in Queues with Non-Stationary Poisson Arrivals
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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 Λ(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 {Λ(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.

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