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On the transient behavior of the repairman problem

Published online by Cambridge University Press:  01 July 2016

Charles Knessl
Charles Knessl*
Affiliation:
University of Illinois at Chicago
*
∗Postal address: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago (MC/249), Chicago, IL 60680, USA.
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Abstract

We consider the repairman problem which corresponds to the finite population M/M/1 queue. Asymptotic approximations for the transient probability distribution of the number of broken machines constructed when the number M of machines is large and the service (repair) rate is also large, specifically, O(M). The approximations are constructed by using singular perturbation techniques such as the ray method, boundary layer theory, and the method of matched asymptotic expansions. Extensive numerical comparisons show the quality of our approximations.

Keywords

TRANSIENT PROBABILITIESSINGULAR PERTURBATIONSRAY METHOD
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 2 , June 1991 , pp. 327 - 354
Copyright
Copyright © Applied Probability Trust 1991 

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