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Stationary Poisson departure processes from non-stationary queues

Published online by Cambridge University Press:  14 July 2016

Robert D. Foley
Robert D. Foley*
Affiliation:
Georgia Institute of Technology
*
∗Postal address: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332–0205, USA.
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Abstract

We present some non-stationary infinite-server queueing systems with stationary Poisson departure processes. In Foley (1982), it was shown that the departure process from the Mt/Gt/∞ queue was a Poisson process, possibly non-stationary. The Mt/Gt/∞ queue is an infinite-server queue with a stationary or non-stationary Poisson arrival process and a general server in which the service time of a customer may depend upon the customer's arrival time. Mirasol (1963) pointed out that the departure process from the M/G/∞ queue is a stationary Poisson process. The question arose whether there are any other Mt/Gt/∞ queueing systems with stationary Poisson departure processes. For example, if the arrival rate is periodic, is it possible to select the service-time distribution functions to fluctuate in order to compensate for the fluctuations of the arrival rate? In this situation and in more general situations, it is possible to select the server such that the system yields a stationary Poisson departure process.

Keywords

POISSON PROCESSPOISSON RANDOM MEASUREINFINITE-SERVER QUEUE
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 1 , March 1986 , pp. 256 - 260
Copyright
Copyright © Applied Probability Trust 1986 

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References

Brown, M. and Ross, S. M. (1969) Some results for infinite server queues. J. Appl. Prob. 6, 604–611.Google Scholar
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Foley, R. D. (1982) The non-homogeneous M/G/8 queue. Opsearch 19, 40–48.Google Scholar
Mirasol, N. M. (1963) The output of an M/G/ß queueing system is Poisson. Operat. Res. 11, 282–284.Google Scholar