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Asymptotics of waiting time distributions in the accumulating priority queue

Author

Listed:
  • Joris Walraevens

    (Ghent University)

  • Thomas Giel

    (Ghent University)

  • Stijn Vuyst

    (Ghent University)

  • Sabine Wittevrongel

    (Ghent University)

Abstract

We analyze the asymptotics of waiting time distributions in the two-class accumulating priority queue with general service times. The accumulating priority queue was suggested by Kleinrock in the 60s—he coined it time-dependent priority—to diversify waiting time objectives of different classes in a paramaterized way. It also avoids the typical starvation problem of regular priority queues. All customers build up priority linearly while waiting in the queue but at a class-dependent rate. At a service opportunity epoch, the customer with highest priority present is served. Stanford and colleagues recently calculated the Laplace–Stieltjes Transform (LST) of the waiting time distributions of the different classes, but only invert these LSTs numerically. In this paper, we analytically calculate the asymptotics of the corresponding distributions from these LSTs. We show that different singularities of the LST can play a role in the asymptotics, depending on the magnitude of service differentiation between both classes.

Suggested Citation

  • Joris Walraevens & Thomas Giel & Stijn Vuyst & Sabine Wittevrongel, 2022. "Asymptotics of waiting time distributions in the accumulating priority queue," Queueing Systems: Theory and Applications, Springer, vol. 101(3), pages 221-244, August.
    • Handle: RePEc:spr:queues:v:101:y:2022:i:3:d:10.1007_s11134-022-09839-7
    DOI: 10.1007/s11134-022-09839-7
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    References listed on IDEAS

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    1. Li, Na & Stanford, David A. & Sharif, Azaz B. & Caron, Richard J. & Pardhan, Alim, 2019. "Optimising key performance indicator adherence with application to emergency department congestion," European Journal of Operational Research, Elsevier, vol. 272(1), pages 313-323.
    2. Na Li & David A. Stanford & Peter Taylor & Ilze Ziedins, 2017. "Nonlinear Accumulating Priority Queues with Equivalent Linear Proxies," Operations Research, INFORMS, vol. 65(6), pages 1712-1721, December.
    3. Tetsuya Takine, 1999. "The Nonpreemptive Priority MAP/G/1 Queue," Operations Research, INFORMS, vol. 47(6), pages 917-927, December.
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    Cited by:

    1. Herwig Bruneel & Arnaud Devos, 2024. "Explicit Solutions for Coupled Parallel Queues," Mathematics, MDPI, vol. 12(15), pages 1-31, July.
    2. A. N. Dudin & S. A. Dudin & O. S. Dudina, 2023. "Randomized Threshold Strategy for Providing Flexible Priority in Multi-Server Queueing System with a Marked Markov Arrival Process and Phase-Type Distribution of Service Time," Mathematics, MDPI, vol. 11(12), pages 1-23, June.
    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.

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