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The M/M/∞ queue in a random environment

Published online by Cambridge University Press:  14 July 2016

C. A. O'Cinneide  and
P. Purdue
C. A. O'Cinneide*
Affiliation:
University of Arkansas
P. Purdue
Affiliation:
University of Kentucky
*
∗Postal address: Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701, USA.
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Abstract

The M/M/∞ queue in a random environment is an infinite-server queue where arrival and service rates are stochastic processes. Here we study the steady-state behavior of such a system. Explicit results are obtained for the factorial moments, the impossibility of a ‘matrix-Poisson' steady-state distribution is demonstrated and two numerical examples are presented.

Keywords

INFINITE-SERVER QUEUESTATIONARY DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 23 , Issue 1 , March 1986 , pp. 175 - 184
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

∗∗

Present address: Probability and Statistics Program, National Science Foundation, Washington, DC 20550, USA.

Research supported in part by NSF grant MCS-8102215–01.

References

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