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An N Server Cutoff Priority Queue Where Arriving Customers Request a Random Number of Servers

Author

Listed:
  • Christian Schaack

    (Harvard Business School, Boston, Massachusetts 02163)

  • Richard C. Larson

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

We consider a multi-priority, N-server, Poisson arrival, nonpreemptive queue, motivated by police applications. The number of servers requested by an arrival has a known priority dependent probability distribution. All servers requested by a customer must start service simultaneously; the servers' service times are independent and exponentially distributed with parameter \mu , independent of priority, server identity or system state. In order to save available servers for higher priority customers, arriving customers of each lower priority are deliberately queued whenever the number of servers busy equals or exceeds a given priority-dependent cutoff number. Whenever all higher priority queues are empty, the longest waiting priority i customer will enter service the instant there is a service completion from a state having precisely N i - k + 1 servers busy, where k is the number of servers requested by the customer and N i is the server cutoff number for priority i. The queueing discipline is in a sense HOL by priorities. We derive the priority i waiting time distribution (in transform domain) and other system statistics. Illustrative computational results are given.

Suggested Citation

  • Christian Schaack & Richard C. Larson, 1989. "An N Server Cutoff Priority Queue Where Arriving Customers Request a Random Number of Servers," Management Science, INFORMS, vol. 35(5), pages 614-634, May.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:5:p:614-634
    DOI: 10.1287/mnsc.35.5.614
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    Cited by:

    1. Iannoni, Ana Paula & Chiyoshi, Fernando & Morabito, Reinaldo, 2015. "A spatially distributed queuing model considering dispatching policies with server reservation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 75(C), pages 49-66.
    2. L. G. Afanaseva & S. A. Grishunina, 2020. "Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 213-241, April.
    3. Schlicher, Loe & Lurkin, Virginie, 2024. "Fighting pickpocketing using a choice-based resource allocation model," European Journal of Operational Research, Elsevier, vol. 315(2), pages 580-595.
    4. 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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