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Insensitivity in queueing systems

Published online by Cambridge University Press:  01 July 2016

David Y. Burman
David Y. Burman*
Affiliation:
Bell Laboratories
*
∗Postal address: Bell Laboratories, Crawfords Corner Road, Holmdel, NJ07733, U.S.A.
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Abstract

It is well known that the stationary distribution of the number of busy servers in the Erlang blocking system (M/G/c/c) depends on the service-time distribution only through its mean. This insensitivity property is shared by several other queueing systems. In this paper, we give simple sufficient conditions for determining if this insensitivity property holds for general queueing systems and related stochastic models. The conditions involve determining whether the solution of the stationary Markovian flow equations also solves certain restricted flow equations. The proof that these conditions are sufficient is direct and elementary.

Keywords

GENERALIZED SEMI-MARKOV PROCESSESINSENSITIVITYLOCAL BALANCEPRODUCT PROPERTY
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 4 , December 1981 , pp. 846 - 859
Copyright
Copyright © Applied Probability Trust 1981 

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