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State Dependence in M / G /1 Server-Vacation Models

Author

Listed:
  • Carl M. Harris

    (George Mason University, Fairfax, Virginia)

  • William G. Marchal

    (University of Toledo, Toledo, Ohio)

Abstract

This paper examines a generalization of the exhaustive and one-at-a-time-discipline M / G /1 server vacation models. This alternative model is viewed as a state-dependent (nonvacation) M / G /1 queue in which the original service times are extended to include a (possibly zero length) state-dependent vacation after each service. Such a vacation policy permits greater flexibility in modeling real problems, and does, in fact, subsume most prior M / G /1 approaches. This device reveals a fundamental decomposition somewhat like that previously established for the classical vacation disciplines. In addition, necessary and sufficient conditions for system ergodicity are established for the state-dependent vacation policy, and some comments are offered on computations.

Suggested Citation

  • Carl M. Harris & William G. Marchal, 1988. "State Dependence in M / G /1 Server-Vacation Models," Operations Research, INFORMS, vol. 36(4), pages 560-565, August.
    • Handle: RePEc:inm:oropre:v:36:y:1988:i:4:p:560-565
    DOI: 10.1287/opre.36.4.560
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    Cited by:

    1. Tian, Naishuo & Zhang, Zhe George, 2006. "A two threshold vacation policy in multiserver queueing systems," European Journal of Operational Research, Elsevier, vol. 168(1), pages 153-163, January.
    2. Vasiliki Kostami, 2020. "Price and Lead time Disclosure Strategies in Inventory Systems," Production and Operations Management, Production and Operations Management Society, vol. 29(12), pages 2760-2788, December.

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