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Approximations for the repairman problem with two repair facilities, I: No spares

Published online by Cambridge University Press:  01 July 2016

Donald L. Iglehart
Affiliation:
Stanford University
Austin J. Lemoine*
Affiliation:
Control Analysis Corporation
*
Now at Clemson University.

Abstract

The model considered here consists of n operating units which are subject to stochastic failure according to an exponential failure time distribution. Failures can be of two types. With probability p(q) a failure is of type 1(2) and is sent to repair facility 1(2) for repair. Repair facility 1(2) operates as a -server queue with exponential repair times having parameter μ1 (μ2). The number of units waiting for or undergoing repair at each of the two facilities is a continuous-parameter Markov chain with finite state space. This paper derives limit theorems for the stationary distribution of this Markov chain as n becomes large under the assumption that both and grow linearly with n. These limit theorems give very useful approximations, in terms of the six parameters characterizing the model, to a distribution that would be difficult to use in practice.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1973 

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Footnotes

Research sponsored by Office of Naval Research contract N00014-72-C-Q266 (NR-347-Q22).

References

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