On the transient behavior of the repairman problem

Authors
Citation
Knessl, Charles, On the transient behavior of the repairman problem, Advances in applied probability , 23(2), 1991, pp. 327-354
ISSN journal
00018678
Volume
23
Issue
2
Year of publication
1991
Pages
327 - 354
Database
ACNP
SICI code
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.