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Whittle index approach to multiserver scheduling with impatient customers and DHR service times

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  • Samuli Aalto

    (Aalto University)

Abstract

We consider the optimal scheduling problem in a multiserver queue with impatient customers belonging to multiple classes. We assume that each customer has a random abandonment time, after which the customer leaves the system if its service has not been completed before that. In addition, we assume that the scheduler is not able to anticipate the expiration of the abandonment times but only knows their distributions and how long each customer has been in the system. Many papers consider this scheduling problem under Poisson arrivals and linear holding costs assuming further that both the service times and the abandonment times have exponential distributions. Even with these additional assumptions, the exact solution is known only in very few special cases. To tackle this tricky problem, we apply the Whittle index approach. Unlike the earlier papers, which were restricted to exponential service times, we allow the service time distributions for which the hazard rate is decreasing. The Whittle index approach is applied to the discrete-time multiserver queueing problem with discounted costs. As our main theoretical result, we prove that the related relaxed optimization problem is indexable and derive the corresponding Whittle index explicitly. Based on this discrete-time result, we develop a reasonable heuristic for the original continuous-time multiserver scheduling problem. The performance of the resulting policy is evaluated in the M/G/M setup by numerical simulations, which demonstrate that it, indeed, gives better performance than the other policies included in the comparison.

Suggested Citation

  • Samuli Aalto, 2024. "Whittle index approach to multiserver scheduling with impatient customers and DHR service times," Queueing Systems: Theory and Applications, Springer, vol. 107(1), pages 1-30, June.
  • Handle: RePEc:spr:queues:v:107:y:2024:i:1:d:10.1007_s11134-024-09902-5
    DOI: 10.1007/s11134-024-09902-5
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    References listed on IDEAS

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    1. S. Bhulai & H. Blok & F. M. Spieksma, 2022. "K competing queues with customer abandonment: optimality of a generalised $$c \mu $$ c μ -rule by the Smoothed Rate Truncation method," Annals of Operations Research, Springer, vol. 317(2), pages 387-416, October.
    2. 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.
    3. 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.
    4. Gang Chen & Jean-Philippe Gayon & Pierre Lemaire, 2023. "Technical Note—Stochastic Scheduling with Abandonment: Necessary and Sufficient Conditions for the Optimality of a Strict Priority Policy," Operations Research, INFORMS, vol. 71(5), pages 1789-1793, September.
    Full references (including those not matched with items on IDEAS)

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