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Service-Level Differentiation in Many-Server Service Systems via Queue-Ratio Routing

Author

Listed:
  • Itai Gurvich

    (Kellogg School of Management, Northwestern University, Evanston, Illinois 60208)

  • Ward Whitt

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

Motivated by telephone call centers, we study large-scale service systems with multiple customer classes and multiple agent pools, each with many agents. To minimize staffing costs subject to service-level constraints, where we delicately balance the service levels (SLs) of the different classes, we propose a family of routing rules called fixed-queue-ratio (FQR) rules. With FQR, a newly available agent next serves the customer from the head of the queue of the class (from among those he is eligible to serve) whose queue length most exceeds a specified proportion of the total queue length. The proportions can be set to achieve desired SL targets. The FQR rule achieves an important state-space collapse (SSC) as the total arrival rate increases, in which the individual queue lengths evolve as fixed proportions of the total queue length. In the current paper we consider a variety of service-level types and exploit SSC to construct asymptotically optimal solutions for the staffing-and-routing problem. The key assumption in the current paper is that the service rates depend only on the agent pool.

Suggested Citation

  • Itai Gurvich & Ward Whitt, 2010. "Service-Level Differentiation in Many-Server Service Systems via Queue-Ratio Routing," Operations Research, INFORMS, vol. 58(2), pages 316-328, April.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:2:p:316-328
    DOI: 10.1287/opre.1090.0736
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    References listed on IDEAS

    as
    1. Avishai Mandelbaum & Alexander L. Stolyar, 2004. "Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cμ-Rule," Operations Research, INFORMS, vol. 52(6), pages 836-855, December.
    2. Jan A. Van Mieghem, 2003. "Due-Date Scheduling: Asymptotic Optimality of Generalized Longest Queue and Generalized Largest Delay Rules," Operations Research, INFORMS, vol. 51(1), pages 113-122, February.
    3. Itay Gurvich & Mor Armony & Avishai Mandelbaum, 2008. "Service-Level Differentiation in Call Centers with Fully Flexible Servers," Management Science, INFORMS, vol. 54(2), pages 279-294, February.
    4. Itay Gurvich & Ward Whitt, 2009. "Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 237-253, June.
    5. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
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