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Scheduling of multi-class multi-server queueing systems with abandonments


  • Urtzi Ayesta

    () (CNRS, LAAS
    IKERBASQUE — Basque Foundation for Science
    Univ. de Toulouse, LAAS
    University of the Basque Country)

  • Peter Jacko

    () (Lancaster University)

  • Vladimir Novak

    () (CERGE-EI, Politickych veznu 7)


Abstract Many real-world situations involve queueing systems in which customers may abandon if service does not start sufficiently quickly. We study a comprehensive model of multi-class queue scheduling accounting for customer abandonment, with the objective of minimizing the total discounted or time-average sum of linear waiting costs, completion rewards, and abandonment penalties of customers in the system. We assume the service times and abandoning times are exponentially distributed. We solve analytically the case in which there is one server and there are one or two customers in the system and obtain an optimal policy. For the general case, we use the framework of restless bandits to analytically design a novel simple index rule with a natural interpretation. We show that the proposed rule achieves near-optimal or asymptotically optimal performance both in single- and multi-server cases, both in overload and underload regimes, and both in idling and non-idling systems.

Suggested Citation

  • Urtzi Ayesta & Peter Jacko & Vladimir Novak, 2017. "Scheduling of multi-class multi-server queueing systems with abandonments," Journal of Scheduling, Springer, vol. 20(2), pages 129-145, April.
  • Handle: RePEc:spr:jsched:v:20:y:2017:i:2:d:10.1007_s10951-015-0456-7
    DOI: 10.1007/s10951-015-0456-7

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    References listed on IDEAS

    1. Oualid Jouini & Auke Pot & Ger Koole & Yves Dallery, 2010. "Online Scheduling Policies for Multiclass Call Centers with Impatient Customers," Post-Print hal-00565528, HAL.
    2. J. Michael Harrison & Assaf Zeevi, 2004. "Dynamic Scheduling of a Multiclass Queue in the Halfin-Whitt Heavy Traffic Regime," Operations Research, INFORMS, vol. 52(2), pages 243-257, April.
    3. Ward Whitt, 2004. "Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments," Management Science, INFORMS, vol. 50(10), pages 1449-1461, October.
    4. P. H. Brill & M. J. M. Posner, 1977. "Level Crossings in Point Processes Applied to Queues: Single-Server Case," Operations Research, INFORMS, vol. 25(4), pages 662-674, August.
    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.
    6. Nam Kyoo Boots & Henk Tijms, 1999. "A Multiserver Queueing System with Impatient Customers," Management Science, INFORMS, vol. 45(3), pages 444-448, March.
    7. Dennis W. Fife, 1965. "Scheduling with Random Arrivals and Linear Loss Functions," Management Science, INFORMS, vol. 11(3), pages 429-437, January.
    8. Jouini, Oualid & Pot, Auke & Koole, Ger & Dallery, Yves, 2010. "Online scheduling policies for multiclass call centers with impatient customers," European Journal of Operational Research, Elsevier, vol. 207(1), pages 258-268, November.
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