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Characterizing the idle-period distribution of GI/G/1 queues

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Jingwen Li  and
Jihong Ou
Jingwen Li
Affiliation:
National University of Singapore
Jihong Ou*
Affiliation:
National University of Singapore
*
∗Postal address: Department of Decision Sciences, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511.
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Abstract

A variety of performance measures of a GI/G/1 queue are explicitly related to the idle-period distribution of the queue, suggesting that the system analysis can be accomplished by the analysis of the idle period. However, the ‘stand-alone' relationship for the idle-period distribution of the GI/G/1 queue (i.e. the counterpart of Lindley's equation) has not been found in the literature. In this paper we develop a non-linear integral equation for the idle period distribution of the GI/G/1 queue. We also show that this non-linear system defines a unique solution. This development makes possible the analysis of the GI/G/1 queue in a different perspective.

Keywords

PREEMPTIVE-RESUME LIFONON-LINEAR INTEGRAL EQUATIONRENEWAL PROCESS

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 247 - 255
Copyright
Copyright © Applied Probability Trust 1995 

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