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Light traffic approximations for regenerative queueing processes

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Chia-Li Wang
Chia-Li Wang*
Affiliation:
National Dong Hwa University
*
*Postal address: Institute of Applied Mathematics, National Dong Hwa University, Hualien, Taiwan, Republic of China.
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Abstract

We consider a regenerative queueing process that is (partially) generated by an embedded phase-type renewal process. We show that, under some specified conditions, a performance measure is an analytic function of the rate of the renewal process. We then develop several methods for deriving its Taylor polynomial in the renewal rate. These polynomials are asymptotically exact as the rate decreases, and, thus, are called light traffic approximations of the performance measure. We show via examples that these new methods are not only more efficient compared to existing ones, but also more versatile due to their general settings, such as to conduct perturbation analysis and study transient behavior.

Keywords

QUEUEING THEORYLIGHT TRAFFIC APPROXIMATIONSREGENERATIVE PROCESSESANALYTIC FUNCTIONS

MSC classification

Primary: 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 4 , December 1997 , pp. 1060 - 1080
Copyright
Copyright © Probability Trust 1997 

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