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Optimal Expulsion Control—A Dual Approach to Admission Control of an Ordered-Entry System

Author

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  • Susan H. Xu

    (Pennsylvania State University, University Park, Pennsylvania)

  • J. George Shanthikumar

    (University of California, Berkeley, California)

Abstract

In this paper we obtain the optimal admission control policy for a first-come, first-served (FCFS) M / M / m ordered-entry queueing system to maximize the expected discounted (and the long-run average) profit (reward minus cost). We introduce a new approach for determining the optimal admission control policy. The underlying idea of this approach is to construct a dual system: a preemptive last-come, first-served (LCFS-P) M / M / m ordered-entry queueing system that is subject to expulsion control . We show that an LCFS-P system with expulsion control is isomorphic to an FCFS system with admission control, and the two systems share the same optimal control policy. Eluding the conventional dynamic programming formulation, we approach the solution from behaviors of individual customers and their impact on the social outcome. This makes our analysis simple and intuitive and reveals a better insight into the structural properties of the optimal control policy. Besides providing formulas to compute the optimal threshold, we use the operational characteristics of the dual system to obtain an easily computable approximation for the optimal threshold. The applicability of the approach transcends well beyond the problem addressed in this paper.

Suggested Citation

  • Susan H. Xu & J. George Shanthikumar, 1993. "Optimal Expulsion Control—A Dual Approach to Admission Control of an Ordered-Entry System," Operations Research, INFORMS, vol. 41(6), pages 1137-1152, December.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:6:p:1137-1152
    DOI: 10.1287/opre.41.6.1137
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    Cited by:

    1. Eitan Altman & Nahum Shimkin, 1998. "Individual Equilibrium and Learning in Processor Sharing Systems," Operations Research, INFORMS, vol. 46(6), pages 776-784, December.
    2. Suresh K. Nair & Ravi Bapna, 2001. "An application of yield management for Internet Service Providers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(5), pages 348-362, August.
    3. Vernon N. Hsu & Susan H. Xu & Boris Jukic, 2009. "Optimal Scheduling and Incentive Compatible Pricing for a Service System with Quality of Service Guarantees," Manufacturing & Service Operations Management, INFORMS, vol. 11(3), pages 375-396, May.
    4. Refael Hassin & Yair Y. Shaki & Uri Yovel, 2015. "Optimal service‐capacity allocation in a loss system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(2), pages 81-97, March.
    5. Refael Hassin & Ran I. Snitkovsky, 2020. "Social and Monopoly Optimization in Observable Queues," Operations Research, INFORMS, vol. 68(4), pages 1178-1198, July.
    6. Bertrand, J. Will M. & van Ooijen, Henny P.G., 2012. "The capacity investment decision for make-to-order production systems with demand rate control," International Journal of Production Economics, Elsevier, vol. 137(2), pages 272-283.

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