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The quasi-stationary distributions of queues in heavy traffic

Published online by Cambridge University Press:  14 July 2016

E. K. Kyprianou
E. K. Kyprianou*
Affiliation:
University of Manchester
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Abstract

This paper demonstrates that, when in heavy traffic, the quasi-stationary distribution of the virtual waiting time process of both the M/G/1 and GI/M/1 queues as well as the quasi-stationary distribution of the waiting times {Wn} of the M/G/1 queue can be approximated by the same gamma distribution. What characterises this approximating gamma distribution are the first two moments of the service time and inter-arrival time distributions only. A similar approximating behaviour is demonstrated for the queue size process.

Keywords

QUASI-STATIONARY DISTRIBUTIONVIRTUAL WAITING TIME PROCESSQUEUE SIZE PROCESSWAITING TIMESIMBEDDED PROCESSESSEQUENCE OF M/G/1 QUEUESSEQUENCE OF GI/M/1 QUEUESHEAVY TRAFFICGAMMA DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 4 , December 1972 , pp. 821 - 831
Copyright
Copyright © Applied Probability Trust 1972 

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References

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