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A Multiserver Queue with Thresholds for the Acceptance of Customers into Service

Author

Listed:
  • Marcel F. Neuts

    (University of Delaware, Newark, Delaware)

  • R. Nadarajan

    (Annamalai University, Annamalainagar, India)

Abstract

A queue with Poisson arrivals is served by N identical exponential servers. When a server becomes free, a group of customers of size at most b can be served. The server is not allowed to process a group of size less than a , 1 ≤ a ≤ b . The actual size of each group served depends on the number of waiting customers. The queue is studied as a Markov process. In the stable case, the stationary probability vector of this process has a simple, readily computable form. Using this form, the stationary waiting time distribution, which is analytically intractable, may be expressed in an algorithmically useful form. Several questions, related to the optimal design of such a service system, may be algorithmically investigated. This model serves to illustrate the advantages of the algorithmic approach. The design criteria are not analytically tractable in general.

Suggested Citation

  • Marcel F. Neuts & R. Nadarajan, 1982. "A Multiserver Queue with Thresholds for the Acceptance of Customers into Service," Operations Research, INFORMS, vol. 30(5), pages 948-960, October.
    • Handle: RePEc:inm:oropre:v:30:y:1982:i:5:p:948-960
    DOI: 10.1287/opre.30.5.948
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    Citations

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    Cited by:

    1. Warren B. Powell, 1987. "Waiting‐time distributions for bulk arrival, bulk service queues with vehicle‐holding and cancellation strategies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 207-227, April.
    2. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    3. S. Chakravarthy & Attahiru Sule Alfa, 1993. "A multiserver queue with markovian arrivals and group services with thresholds," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(6), pages 811-827, October.

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