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The non-renewal nature of the quasi-input process in the M/G/1/∞ queue

Published online by Cambridge University Press:  14 July 2016

Jeffrey J. Hunter
Jeffrey J. Hunter*
Affiliation:
University of Auckland
*
∗Postal address: Department of Mathematics and Statistics, University of Auckland, Private Bag, Auckland, New Zealand.
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Abstract

Falin (1984) examined the quasi-input process (the flow of service starting times) in the M/G/1/∞ queue and raised the question as to whether this process is a renewal process. We show that, except in the trivial case of instantaneous service, the quasi-input process is never renewal.

Keywords

QUEUEING THEORYRANDOM FLOWSMARKOV RENEWAL PROCESSESRENEWAL PROCESSESSTATIONARY DISTRIBUTIONS
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 803 - 811
Copyright
Copyright © Applied Probability Trust 1986 

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References

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