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ON THE LAW OF THE iTH WAITING TIME IN A BUSY PERIOD OF G/M/c QUEUES

Published online by Cambridge University Press:  18 December 2007

Opher Baron
Opher Baron
Affiliation:
Rotman School of Management University of Toronto Toronto, ON, Canada M5S 3E6 E-mail: opher.baron@rotman.utoronto.ca
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Abstract

We use induction to derive the distribution of the waiting time of the ith waiting customer in a busy period for a G/M/1 queue with a first come–first serve service. A trivial implication gives the law for the ith waiting time in a busy period for a G/M/c queue. Finally, we use the Lindley recursion to relate our results to the distribution of random walks.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 1 , January 2008 , pp. 75 - 80
Copyright
Copyright © Cambridge University Press 2008

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