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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
Affiliation:
Case Western Reserve University

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, ∞).

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1977 

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References

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