A globally gated polling system with server interruptions, and applications to the repairman problem

O. J. Boxma, J. A. Weststrate, U. Yechiali

Research output: Contribution to journalArticlepeer-review

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 so-called elevator-type polling scheme mean waiting times of preventive maintenance jobs at all installations are equal.

Original languageEnglish
Pages (from-to)187-208
Number of pages22
JournalProbability in the Engineering and Informational Sciences
Volume7
Issue number2
DOIs
StatePublished - 1993

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