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Optimal time to repair a broken server

Published online by Cambridge University Press:  01 July 2016

Awi Federgruen  and
Kut C. So
Awi Federgruen*
Affiliation:
Columbia University
Kut C. So*
Affiliation:
AT&T Bell Laboratories
*
∗Postal address: Graduate School of Business. 412 Uris Hall, Columbia University, New York, NY 10027, USA. Research partly supported by NSF Grant no. ECS-8604409, and partly carried out at the Hebrew University, Jerusalem.
∗∗Postal address: AT&T, Bell Laboratories, P.O. Box 900, Princeton, NJ 08540, USA.
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Abstract

We consider a single-server queueing system with Poisson arrivals and general service times. While the server is up, it is subject to breakdowns according to a Poisson process. When the server breaks down, we may either repair the server immediately or postpone the repair until some future point in time. The operating costs of the system include customer holding costs, repair costs and running costs. The objective is to find a corrective maintenance policy which minimizes the long-run average operating costs of the system. The problem is formulated as a semi-Markov decision process. Under some mild conditions on the repair time and service time distributions and the customer holding cost rate function, we prove that there exists an optimal stationary policy which is characterized by a single threshold parameter: a repair is initiated if and only if the number of customers in the system exceeds this threshold. We also show how the average cost under such policies may be computed and how an optimal policy may efficiently be determined.

Keywords

QUEUES WITH BREAKDOWNSSEMI-MARKOV DECISION PROCESSCORRECTIVE MAINTENANCE POLICYMONOTONE POLICIES
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 2 , June 1989 , pp. 376 - 397
Copyright
Copyright © Applied Probability Trust 1989 

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