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The c(mu)/(theta) Rule for Many-Server Queues with Abandonment

Author

Listed:
  • Rami Atar

    (Department of Electrical Engineering, Technion--Israel Institute of Technology, Haifa 32000, Israel)

  • Chanit Giat

    (Department of Electrical Engineering, Technion--Israel Institute of Technology, Haifa 32000, Israel)

  • Nahum Shimkin

    (Department of Electrical Engineering, Technion--Israel Institute of Technology, Haifa 32000, Israel)

Abstract

We consider a multiclass queueing system with multiple homogeneous servers and customer abandonment. For each customer class i , the holding cost per unit time, the service rate, and the abandonment rate are denoted by c i , (mu) i , and (theta) i , respectively. We prove that under a many-server fluid scaling and overload conditions, a server-scheduling policy that assigns priority to classes according to their index c i (mu) i / (theta) i is asymptotically optimal for minimizing the overall long-run average holding cost. An additional penalty on customer abandonment is easily incorporated into this model and leads to a similar index rule.

Suggested Citation

  • Rami Atar & Chanit Giat & Nahum Shimkin, 2010. "The c(mu)/(theta) Rule for Many-Server Queues with Abandonment," Operations Research, INFORMS, vol. 58(5), pages 1427-1439, October.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:5:p:1427-1439
    DOI: 10.1287/opre.1100.0826
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    References listed on IDEAS

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    1. Ward Whitt, 2004. "Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments," Management Science, INFORMS, vol. 50(10), pages 1449-1461, October.
    2. 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.
    3. 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.
    4. 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.
    5. Ward Whitt, 2006. "Fluid Models for Multiserver Queues with Abandonments," Operations Research, INFORMS, vol. 54(1), pages 37-54, February.
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    Cited by:

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    3. Rami Atar & Haya Kaspi & Nahum Shimkin, 2014. "Fluid Limits for Many-Server Systems with Reneging Under a Priority Policy," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 672-696, August.
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    7. Samim Ghamami & Amy R. Ward, 2013. "Dynamic Scheduling of a Two-Server Parallel Server System with Complete Resource Pooling and Reneging in Heavy Traffic: Asymptotic Optimality of a Two-Threshold Policy," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 761-824, November.

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