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Fluid limit for a multi-server, multiclass random order of service queue with reneging and tracking of residual patience times

Author

Listed:
  • Eva H. Loeser

    (University of California, San Diego
    University of North Carolina, Chapel Hill)

  • Ruth J. Williams

    (University of California, San Diego)

Abstract

In this paper, we consider a multi-server, multiclass queue with reneging operating under the random order of service discipline. Interarrival times, service times, and patience times are assumed to be generally distributed. Under mild conditions, we establish a fluid limit theorem for a measure-valued process that keeps track of the remaining patience time for each job in the queue, when the number of servers and classes is held fixed. We prove uniqueness for fluid model solutions in all but one case. We characterize the unique invariant state for the fluid model and prove that fluid model solutions converge to the invariant state as time goes to infinity, uniformly for suitable initial conditions.

Suggested Citation

  • Eva H. Loeser & Ruth J. Williams, 2025. "Fluid limit for a multi-server, multiclass random order of service queue with reneging and tracking of residual patience times," Queueing Systems: Theory and Applications, Springer, vol. 109(2), pages 1-78, June.
    • Handle: RePEc:spr:queues:v:109:y:2025:i:2:d:10.1007_s11134-025-09941-6
    DOI: 10.1007/s11134-025-09941-6
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    References listed on IDEAS

    as
    1. Amber L. Puha & Amy R. Ward, 2022. "Fluid Limits for Multiclass Many-Server Queues with General Reneging Distributions and Head-of-the-Line Scheduling," Mathematics of Operations Research, INFORMS, vol. 47(2), pages 1192-1228, May.
    2. W. Rogiest & K. Laevens & J. Walraevens & H. Bruneel, 2015. "Random-order-of-service for heterogeneous customers: waiting time analysis," Annals of Operations Research, Springer, vol. 226(1), pages 527-550, March.
    3. Elene Anton & Urtzi Ayesta & Matthieu Jonckheere & Ina Maria Verloop, 2021. "On the Stability of Redundancy Models," Operations Research, INFORMS, vol. 69(5), pages 1540-1565, September.
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