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The covariance function of the virtual waiting-time process in an M/G/1 queue

Published online by Cambridge University Press:  01 July 2016

Teunis J. Ott
Teunis J. Ott*
Affiliation:
Case Western Reserve University
*
∗Now at the University of Texas at Dallas.
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Abstract

Let R(t) be the covariance function of the stationary virtual waiting-time process of a stable M/G/1 queue. It is proven that if R(t) exists, i.e., if the service-times have a finite third moment, then R(t) is positive and convex on [0, ∞), with an absolutely continuous derivative R’ and a bounded, non-negative second derivative R″. Also, and R″ cannot be chosen monotone. Contrary to a finding by Beneš [1] it is proven that if and only if the service-times have a finite fourth moment.

Keywords

QUEUEING THEORYM/G/1 QUEUESVIRTUAL WAITING-TIME PROCESSESCOVARIANCE FUNCTIONS
Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 1 , March 1977 , pp. 158 - 168
Copyright
Copyright © Applied Probability Trust 1977 

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References

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