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Optimal Dynamic Assignment of Customers to Heterogeneous Servers in Parallel

Author

Listed:
  • Susan H. Xu

    (Pennsylvania State University, University Park, Pennsylvania)

  • Rhonda Righter

    (Santa Clara University, Santa Clara, California)

  • J. George Shanthikumar

    (University of California, Berkeley, California)

Abstract

The system under consideration comprises two classes of customers to be served by two stations, with parallel servers in each station. While class-1 customers can only receive service from station 1, class-2 customers can be served by either station. Arrival processes of customers form two mutually independent Poisson processes. The service time of a customer at either station is exponentially distributed with a common rate. A class- i customer, while present in the system, will incur a holding cost h i with h 1 ≥ h 2 . The objective is to dynamically assign customers to idle servers so that the expected discounted (or the long-run average) holding cost is minimized. We show that a class- j customer should be assigned to an idle server in station j , j = 1, 2, whenever possible, and a class-2 customer should be assigned to an idle server in station 1 only if (no class-1 customers are waiting, and) the length of queue 2 exceeds a critical number. Moreover, the critical number is monotonically increasing in the number of busy servers in station 1. The numerical results for some test cases are reported.

Suggested Citation

  • Susan H. Xu & Rhonda Righter & J. George Shanthikumar, 1992. "Optimal Dynamic Assignment of Customers to Heterogeneous Servers in Parallel," Operations Research, INFORMS, vol. 40(6), pages 1126-1138, December.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:6:p:1126-1138
    DOI: 10.1287/opre.40.6.1126
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    Cited by:

    1. Heng-Li Liu & Quan-Lin Li, 2023. "Matched Queues with Flexible and Impatient Customers," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    2. Elena Fernández & Yolanda Hinojosa & Justo Puerto, 2005. "Filtering Policies in Loss Queuing Network Location Problems," Annals of Operations Research, Springer, vol. 136(1), pages 259-283, April.
    3. Zhang, Zhongju & Daigle, John, 2012. "Analysis of job assignment with batch arrivals among heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 217(1), pages 149-161.
    4. Wyean Chan & Ger Koole & Pierre L'Ecuyer, 2014. "Dynamic Call Center Routing Policies Using Call Waiting and Agent Idle Times," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 544-560, October.
    5. D. P. Song & Y. X. Sun & W. Xing, 1998. "Optimal Control of a Stochastic Assembly Production Line," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 681-700, September.
    6. Linn Sennott, 1997. "On computing average cost optimal policies with application to routing to parallel queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(1), pages 45-62, February.
    7. Ari Arapostathis & Guodong Pang, 2018. "Infinite-Horizon Average Optimality of the N-Network in the Halfin–Whitt Regime," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 838-866, August.
    8. Delasay, Mohammad & Kolfal, Bora & Ingolfsson, Armann, 2012. "Maximizing throughput in finite-source parallel queue systems," European Journal of Operational Research, Elsevier, vol. 217(3), pages 554-559.
    9. Keumseok Kang & J. George Shanthikumar & Kemal Altinkemer, 2016. "Postponable Acceptance and Assignment: A Stochastic Dynamic Programming Approach," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 493-508, October.

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