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The stable M/G/1 queue in heavy traffic and its covariance function

Published online by Cambridge University Press:  01 July 2016

Teunis J. Ott
Teunis J. Ott*
Affiliation:
Case Western Reserve University
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Abstract

Let X(t) be the virtual waiting-time process of a stable M/G/1 queue. Let R(t) be the covariance function of the stationary process X(t), B(t) the busy-period distribution of X(t); and let E(t) = P{X(t) = 0|X(0) = 0}.

For X(t) some heavy-traffic results are given, among which are limiting expressions for R(t) and its derivatives and for B(t) and E(t).

These results are used to find the covariance function of stationary Brownian motion on [0, ∞).

Keywords

QUEUEING THEORYM/G/1 QUEUEHEAVY TRAFFIC APPROXIMATIONSVIRTUAL WAITING-TIME PROCESSESCOVARIANCE FUNCTIONS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 1 , March 1977 , pp. 169 - 186
Copyright
Copyright © Applied Probability Trust 1977 

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