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Lévy-driven GPS queues with heavy-tailed input

Author

Listed:
  • Krzysztof Dȩbicki

    (University of Wrocław)

  • Peng Liu

    (University of Wrocław
    University of Lausanne, UNIL-Dorigny)

  • Michel Mandjes

    (University of Amsterdam)

  • Iwona Sierpińska-Tułacz

    (University of Wrocław)

Abstract

In this paper, we derive exact large buffer asymptotics for a two-class generalized processor sharing (GPS) model, under the assumption that the input traffic streams generated by both classes correspond to heavy-tailed Lévy processes. Four scenarios need to be distinguished, which differ in terms of (i) the level of heavy-tailedness of the driving Lévy processes as well as (ii) the values of the corresponding mean rates relative to the GPS weights. The derived results are illustrated by two important special cases, in which the queues’ inputs are modeled by heavy-tailed compound Poisson processes and by $$\alpha $$ α -stable Lévy motions.

Suggested Citation

  • Krzysztof Dȩbicki & Peng Liu & Michel Mandjes & Iwona Sierpińska-Tułacz, 2017. "Lévy-driven GPS queues with heavy-tailed input," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 249-267, April.
    • Handle: RePEc:spr:queues:v:85:y:2017:i:3:d:10.1007_s11134-016-9510-1
    DOI: 10.1007/s11134-016-9510-1
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    References listed on IDEAS

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    1. Willekens, Eric, 1987. "On the supremum of an infinitely divisible process," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 173-175.
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