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Virtual allocation policies for many-server queues with abandonment

Author

Listed:
  • Zhenghua Long

    (Nanjing University
    The Hong Kong University of Science and Technology)

  • Jiheng Zhang

    (Nanjing University)

Abstract

We study a multiclass many-server queueing system with renewal arrivals and generally distributed service and patience times under a nonpreemptive allocation policy. The status of the system is described by a pair of measure-valued processes to track the residual service and patience times of customers in each class. We establish fluid approximations and study the long-term behavior of the fluid model. The equilibrium state of the fluid model leads to a nonlinear program, which enables us to identify a lower bound for the long-run expected total holding and abandonment costs and design an allocation policy to achieve this lower bound. The optimality of the proposed policy is also demonstrated via numerical experiments.

Suggested Citation

  • Zhenghua Long & Jiheng Zhang, 2019. "Virtual allocation policies for many-server queues with abandonment," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 399-451, December.
  • Handle: RePEc:spr:mathme:v:90:y:2019:i:3:d:10.1007_s00186-019-00683-9
    DOI: 10.1007/s00186-019-00683-9
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    References listed on IDEAS

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    1. Itay Gurvich & Ward Whitt, 2009. "Queue-and-Idleness-Ratio Controls in Many-Server Service Systems," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 363-396, May.
    2. Ward Whitt, 2004. "Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments," Management Science, INFORMS, vol. 50(10), pages 1449-1461, October.
    3. 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.
    4. 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.
    5. Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2006. "Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method," Operations Research, INFORMS, vol. 54(3), pages 419-435, June.
    6. Tolga Tezcan, 2008. "Optimal Control of Distributed Parallel Server Systems Under the Halfin and Whitt Regime," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 51-90, February.
    7. Achal Bassamboo & Ramandeep Singh Randhawa, 2016. "Scheduling Homogeneous Impatient Customers," Management Science, INFORMS, vol. 62(7), pages 2129-2147, July.
    8. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    9. Achal Bassamboo & Ramandeep S. Randhawa, 2010. "On the Accuracy of Fluid Models for Capacity Sizing in Queueing Systems with Impatient Customers," Operations Research, INFORMS, vol. 58(5), pages 1398-1413, October.
    10. Ward Whitt, 2006. "Fluid Models for Multiserver Queues with Abandonments," Operations Research, INFORMS, vol. 54(1), pages 37-54, February.
    11. Ohad Perry & Ward Whitt, 2011. "A Fluid Approximation for Service Systems Responding to Unexpected Overloads," Operations Research, INFORMS, vol. 59(5), pages 1159-1170, October.
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