Correlated M/G/1-type queue with randomized server repair and maintenance modes

David Perry, M. J.M. Posner

Research output: Contribution to journalArticlepeer-review


We consider a single machine, subject to breakdown, that produces items to inventory, continuously and uniformly. While the machine is working (an ON period), there is a deterministic net flow into the buffer. There are also two different types of OFF periods; one is a repair operation initiated after a breakdown, and the other is a preventive maintenance operation. The length of an OFF period depends on the length of the preceding ON period. During OFF periods there is a uniform outflow from the inventory buffer. The buffer content process can then be described as a fluid model. The main tool employed in determining its steady-state law exploits an equivalence relationship between the buffer content process and the virtual waiting time process of a special single-server queue in which the interarrival times and the service requirements depend on each other. We present an appropriate cost function and provide an optimization scheme illustrated by some numerical results.

Original languageEnglish
Pages (from-to)137-147
Number of pages11
JournalOperations Research Letters
Issue number3
StatePublished - Apr 2000

Bibliographical note

Funding Information:
We wish to thank O.J. Boxma for his careful reading of the manuscript and for providing useful comments and suggestions. Also, the financial support of the Natural Sciences and Engineering Research Council of Canada under grant OGP0004374 is gratefully appreciated.

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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