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A Globally Gated Polling System with Server Interruptions, and Applications to the Repairman Problem

Published online by Cambridge University Press:  27 July 2009

O. J. Boxma ,
J. A. Weststrate  and
U. Yechiali
O. J. Boxma
Affiliation:
Centre for Mathematics and Computer ScienceP.O. Box 4079, 1009 AB Amsterdam, The Netherlands*; Faculty of Economics, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands
J. A. Weststrate
Affiliation:
Faculty of Economics, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands
U. Yechiali
Affiliation:
Department of Statistics, School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
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Abstract

A repair crew is responsible for the maintenance and operation of N installations. The crew has to perform a collection of preventive maintenance tasks at the various installations. The installations may break down from time to time, generating corrective maintenance requests which have priority over the preventive maintenance tasks. We formulate and analyze this real-world problem as a single-server multi-queue polling model with Globally Gated service discipline and with server interruptions. We derive closed-form expressions for the Laplace-Stieltjes Transform and the first moment of the waiting time distributions of the preventive and corrective maintenance requests at the various installations, and obtain simple and easily implementable static and dynamic rules for optimal operation of the system. We further show that, for the socalled elevator-type polling scheme, mean waiting times of preventive maintenance jobs at all installations are equal.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 2 , April 1993 , pp. 187 - 208
Copyright
Copyright © Cambridge University Press 1993

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