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On multiple priority multi-server queues with impatience

Author

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  • O Jouini

    (1] Laboratoire Génie Industriel, Ecole Centrale Paris, Châtenay-Malabry, France[2] Rouen Business School, Mont Saint Aignan Cedex, France)

  • A Roubos

    (VU University Amsterdam, Amsterdam, The Netherlands)

Abstract

We consider Markovian multi-server queues with two types of impatient customers: high- and low-priority ones. The first type of customer has a non-preemptive priority over the other type. After entering the queue, a customer will wait a random length of time for service to begin. If service has not begun by this time he or she will abandon and be lost. We consider two cases where the discipline of service within each customer type is first-come first-served (FCFS) or last-come first-served (LCFS). For each type of customer, we focus on various performance measures related to queueing delays: unconditional waiting times, and conditional waiting times given service and given abandonment. The analysis we develop holds also for a priority queue with mixed policies, that is, FCFS for the first type and LCFS for the second one, and vice versa. We explicitly derive the Laplace–Stieltjes transforms of the defined random variables. In addition we show how to extend the analysis to more than two customer types. Finally we compare FCFS and LCFS and gain insights through numerical experiments.

Suggested Citation

  • O Jouini & A Roubos, 2014. "On multiple priority multi-server queues with impatience," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(5), pages 616-632, May.
    • Handle: RePEc:pal:jorsoc:v:65:y:2014:i:5:p:616-632
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    Citations

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    Cited by:

    1. Yacov Satin & Rostislav Razumchik & Ivan Kovalev & Alexander Zeifman, 2023. "Ergodicity and Related Bounds for One Particular Class of Markovian Time—Varying Queues with Heterogeneous Servers and Customer’s Impatience," Mathematics, MDPI, vol. 11(9), pages 1-15, April.
    2. Ivo Adan & Brett Hathaway & Vidyadhar G. Kulkarni, 2019. "On first-come, first-served queues with two classes of impatient customers," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 113-142, February.
    3. Konstantin Samouylov & Olga Dudina & Alexander Dudin, 2023. "Analysis of Multi-Server Queueing System with Flexible Priorities," Mathematics, MDPI, vol. 11(4), pages 1-22, February.
    4. Hideaki Takagi, 2016. "Waiting time in the M/M/ $$ m $$ m LCFS nonpreemptive priority queue with impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 257-289, December.
    5. Mingang Yin & Ming Yan & Yu Guo & Minghe Liu, 2023. "Analysis of a Pre-Emptive Two-Priority Queuing System with Impatient Customers and Heterogeneous Servers," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    6. Bolandifar, Ehsan & DeHoratius, Nicole & Olsen, Tava, 2023. "Modeling abandonment behavior among patients," European Journal of Operational Research, Elsevier, vol. 306(1), pages 243-254.

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