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On preemptive-repeat LIFO queues

Author

Listed:
  • Søren Asmussen

    (Ny Munkegade)

  • Peter W. Glynn

    (Stanford University)

Abstract

In this paper, we study the basic properties of last-in first-out (LIFO) preemptive-repeat single-server queues in which the server needs to start service from scratch whenever a preempted customer reaches the server. In particular, we study the question of when such queues are stable (in the sense that the equilibrium time-in-system is finite-valued with probability one) and show how moments of the equilibrium customer sojourn time can be computed when the system is stable. A complete analysis of stability is provided in the setting of Poisson arrivals and in that of the Markovian arrival process. The stability region depends upon the detailed structure of the interarrival and service time distributions and cannot be expressed purely in terms of expected values. This is connected to the fact that such preemptive-repeat queues are not work conserving.

Suggested Citation

  • Søren Asmussen & Peter W. Glynn, 2017. "On preemptive-repeat LIFO queues," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 1-22, October.
    • Handle: RePEc:spr:queues:v:87:y:2017:i:1:d:10.1007_s11134-017-9532-3
    DOI: 10.1007/s11134-017-9532-3
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    References listed on IDEAS

    as
    1. B. Avi-Itzhak, 1963. "Preemptive Repeat Priority Queues as a Special Case of the Multipurpose Server Problem---I," Operations Research, INFORMS, vol. 11(4), pages 597-609, August.
    2. B. Avi-Itzhak, 1963. "Preemptive Repeat Priority Queues as a Special Case of the Multipurpose Server Problem---II," Operations Research, INFORMS, vol. 11(4), pages 610-619, August.
    3. Søren Asmussen & Pierre Fiorini & Lester Lipsky & Tomasz Rolski & Robert Sheahan, 2008. "Asymptotic Behavior of Total Times for Jobs That Must Start Over if a Failure Occurs," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 932-944, November.
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