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Shadow-Routing Based Control of Flexible Multiserver Pools in Overload

Author

Listed:
  • Alexander L. Stolyar

    (Bell Labs, Alcatel-Lucent, Murray Hill, New Jersey 07974)

  • Tolga Tezcan

    (Simon Graduate School of Business, University of Rochester, Rochester, New York 14627)

Abstract

We consider a general parallel server system model with multiple customer classes and several flexible multiserver pools, in the many-server asymptotic regime where the input rates and server pool sizes are scaled up linearly to infinity. Service of a customer brings a constant reward, which depends on its class. The objective is to maximize the long-run reward rate. Our primary focus is on overloaded systems. Unlike in the case when the system is not overloaded, where the main decision is how to allocate resources to incoming customers, in this case it is also crucial to determine which customers will be admitted to the system. We propose a real-time, parsimonious, robust routing policy, SHADOW-RM, which does not require the knowledge of customer input rates and does not solve any optimization problem explicitly, and we prove its asymptotic optimality. Then, by combining SHADOW-RM with another policy, SHADOW-LB, proposed in our previous work for systems that are not overloaded, we suggest policy SHADOW-TANDEM, which automatically and seamlessly detects overload and reduces to one of the schemes, SHADOW-RM or SHADOW-LB, accordingly. Extensive simulations demonstrate a remarkably good performance of proposed policies.

Suggested Citation

  • Alexander L. Stolyar & Tolga Tezcan, 2011. "Shadow-Routing Based Control of Flexible Multiserver Pools in Overload," Operations Research, INFORMS, vol. 59(6), pages 1427-1444, December.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:6:p:1427-1444
    DOI: 10.1287/opre.1110.0960
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    References listed on IDEAS

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    Cited by:

    1. J. G. Dai & Pengyi Shi, 2019. "Inpatient Overflow: An Approximate Dynamic Programming Approach," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 894-911, October.
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    3. Tolga Tezcan & Banafsheh Behzad, 2012. "Robust Design and Control of Call Centers with Flexible Interactive Voice Response Systems," Manufacturing & Service Operations Management, INFORMS, vol. 14(3), pages 386-401, July.
    4. Jim G. Dai & Pengyi Shi, 2021. "Recent Modeling and Analytical Advances in Hospital Inpatient Flow Management," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1838-1862, June.
    5. Alexander L. Stolyar, 2013. "An Infinite Server System with General Packing Constraints," Operations Research, INFORMS, vol. 61(5), pages 1200-1217, October.
    6. Michael F. Kamali & Tolga Tezcan & Ozlem Yildiz, 2019. "When to Use Provider Triage in Emergency Departments," Management Science, INFORMS, vol. 65(3), pages 1003-1019, March.
    7. Silviya Valeva & Guodong Pang & Andrew J. Schaefer & Gilles Clermont, 2023. "Acuity-Based Allocation of ICU-Downstream Beds with Flexible Staffing," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 403-422, March.

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