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Large deviations for stochastic fluid networks with Weibullian tails

Author

Listed:
  • Mihail Bazhba

    (UvA)

  • Chang-Han Rhee

    (Northwestern University)

  • Bert Zwart

    (Centrum Wiskunde Informatica
    Eindhoven University of Technology)

Abstract

We consider a stochastic fluid network where the external input processes are compound Poisson with heavy-tailed Weibullian jumps. Our results comprise of large deviations estimates for the buffer content process in the vector-valued Skorokhod space which is endowed with the product $$J_1$$ J 1 topology. To illustrate our framework, we provide explicit results for a tandem queue. At the heart of our proof is a recent sample-path large deviations result, and a novel continuity result for the Skorokhod reflection map in the product $$J_1$$ J 1 topology.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:102:y:2022:i:1:d:10.1007_s11134-022-09865-5
    DOI: 10.1007/s11134-022-09865-5
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    References listed on IDEAS

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    1. Bohan Chen & Jose Blanchet & Chang-Han Rhee & Bert Zwart, 2019. "Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 919-942, August.
    2. 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.
    3. Masakiyo Miyazawa, 2011. "Light tail asymptotics in multidimensional reflecting processes for queueing networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 233-299, December.
    4. 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.
    5. Masakiyo Miyazawa, 2011. "Rejoinder on: Light tail asymptotics in multidimensional reflecting processes for queueing networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 313-316, December.
    Full references (including those not matched with items on IDEAS)

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