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The Computation of Optimal Control Limits for a Queue with Batch Services

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  • Howard J. Weiss

    (Temple University)

Abstract

We study the optimal control of a queueing system with Poisson input and a server capable of serving an infinite number of customers per batch. It is known that the optimal type of control policy is a control limit policy: service should begin if and only if the number of waiting customers is at least as large as some control limit. Our objective is to find the control limit that minimizes the long run average cost of waiting and service charges. We determine the cost as a function of the control limit, present properties of the cost function and optimal control limit, present easily computable upper and lower bounds for the optimal control limit and an algorithm for finding the optimal control limit.

Suggested Citation

  • Howard J. Weiss, 1979. "The Computation of Optimal Control Limits for a Queue with Batch Services," Management Science, INFORMS, vol. 25(4), pages 320-328, April.
    • Handle: RePEc:inm:ormnsc:v:25:y:1979:i:4:p:320-328
    DOI: 10.1287/mnsc.25.4.320
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    Cited by:

    1. Lotfi Tadj & Gautam Choudhury, 2005. "Optimal design and control of queues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 359-412, December.
    2. Oguzhan Alagoz & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2004. "The Optimal Timing of Living-Donor Liver Transplantation," Management Science, INFORMS, vol. 50(10), pages 1420-1430, October.
    3. Oguzhan Alagoz & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2007. "Determining the Acceptance of Cadaveric Livers Using an Implicit Model of the Waiting List," Operations Research, INFORMS, vol. 55(1), pages 24-36, February.
    4. Olga Bountali & Antonis Economou, 2019. "Strategic customer behavior in a two-stage batch processing system," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 3-29, October.
    5. Stein, William E. & Rapoport, Amnon & Seale, Darryl A. & Zhang, Hongtao & Zwick, Rami, 2007. "Batch queues with choice of arrivals: Equilibrium analysis and experimental study," Games and Economic Behavior, Elsevier, vol. 59(2), pages 345-363, May.
    6. Jansen, J.B., 1998. "Service and inventory models subject to a delay-limit," Other publications TiSEM d51b1fee-e8a2-46bc-b331-1, Tilburg University, School of Economics and Management.

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