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An N -Server Cutoff Priority Queue

Author

Listed:
  • Christian Schaack

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Richard C. Larson

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

We consider a multi-priority, nonpreemptive, multi-server queueing system, with Poisson arrivals and negative exponential service times. In order to save available servers for higher priority customers, the system deliberately queues arriving lower priority customers whenever the number of busy servers equals or exceeds a given priority-dependent cutoff number. A queued, priority i customer enters service the instant there are fewer than the respective cutoff number of servers busy and all higher priority queues are empty. We derive several performance measures for the waiting time of the i th priority class: its mean, its second moment, and its distribution (in transforms). We also extend the analysis to systems in which any subset of priority levels may overflow to some other system rather than join infinite capacity queues.

Suggested Citation

  • Christian Schaack & Richard C. Larson, 1986. "An N -Server Cutoff Priority Queue," Operations Research, INFORMS, vol. 34(2), pages 257-266, April.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:2:p:257-266
    DOI: 10.1287/opre.34.2.257
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    Cited by:

    1. Diwakar Gupta & Lei Wang, 2008. "Revenue Management for a Primary-Care Clinic in the Presence of Patient Choice," Operations Research, INFORMS, vol. 56(3), pages 576-592, June.
    2. Soovin Yoon & Laura A. Albert, 2018. "An expected coverage model with a cutoff priority queue," Health Care Management Science, Springer, vol. 21(4), pages 517-533, December.
    3. Iannoni, Ana P. & Morabito, Reinaldo, 2023. "A review on hypercube queuing model's extensions for practical applications," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    4. Noah Gans & Yong-Pin Zhou, 2003. "A Call-Routing Problem with Service-Level Constraints," Operations Research, INFORMS, vol. 51(2), pages 255-271, April.
    5. Yoon, Soovin & Albert, Laura A., 2021. "Dynamic dispatch policies for emergency response with multiple types of vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).

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