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The Correlation Coefficients of the Queue Lengths of Some Stationary Single Server Queues

Published online by Cambridge University Press:  09 April 2009

A. G. Pakes
A. G. Pakes
Affiliation:
Department of Mathematics Monash UniversityMelbourne, Australia
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Until recently there has been little systematic work on the second-order properties of queueing processes. The aim of this paper is to study systematically the second-order properties of the queue length processes embedded at departure epochs in the M/G/1 and bulk service M/G/1 queues, and at arrival epochs in the GI/M/1 queue. In the latter case our results extend those of Daley [7], while in the ordinary M/G/1 queue our work parallels Daley's [6] discussion of waiting times in the same system. In the final section we briefly discuss two discrete time queueing systems.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1971 , pp. 35 - 46
Copyright
Copyright © Australian Mathematical Society 1971

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