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Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times

Author

Listed:
  • Mihail Bazhba

    (Centrum Wiskunde & Informatica)

  • Jose Blanchet

    (Stanford University 475 Via Ortega)

  • Chang-Han Rhee

    (Northwestern University)

  • Bert Zwart

    (Centrum Wiskunde & Informatica
    Eindhoven University of Technology)

Abstract

We study the occurrence of large queue lengths in the GI / GI / d queue with heavy-tailed Weibull-type service times. Our analysis hinges on a recently developed sample path large-deviations principle for Lévy processes and random walks, following a continuous mapping approach. Also, we identify and solve a key variational problem which provides physical insight into the way a large queue length occurs. In contrast to the regularly varying case, we observe several subtle features such as a non-trivial trade-off between the number of big jobs and their sizes and a surprising asymmetric structure in asymptotic job sizes leading to congestion.

Suggested Citation

  • Mihail Bazhba & Jose Blanchet & Chang-Han Rhee & Bert Zwart, 2019. "Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times," Queueing Systems: Theory and Applications, Springer, vol. 93(3), pages 195-226, December.
    • Handle: RePEc:spr:queues:v:93:y:2019:i:3:d:10.1007_s11134-019-09640-z
    DOI: 10.1007/s11134-019-09640-z
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    References listed on IDEAS

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    1. Sergey Foss & Dmitry Korshunov, 2012. "On Large Delays in Multi-Server Queues with Heavy Tails," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 201-218, May.
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    Cited by:

    1. Mihail Bazhba & Chang-Han Rhee & Bert Zwart, 2022. "Large deviations for stochastic fluid networks with Weibullian tails," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 25-52, October.

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