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Speed of convergence to the quasi-stationary distribution for Lévy input fluid queues

Author

Listed:
  • Zbigniew Palmowski

    (Wrocław University of Science and Technology)

  • Maria Vlasiou

    (Eindhoven University of Technology)

Abstract

In this note, we prove that the speed of convergence of the workload of a Lévy-driven queue to the quasi-stationary distribution is of order 1/t. We identify also the Laplace transform of the measure giving this speed and provide some examples.

Suggested Citation

  • Zbigniew Palmowski & Maria Vlasiou, 2020. "Speed of convergence to the quasi-stationary distribution for Lévy input fluid queues," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 153-167, October.
    • Handle: RePEc:spr:queues:v:96:y:2020:i:1:d:10.1007_s11134-020-09664-w
    DOI: 10.1007/s11134-020-09664-w
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    References listed on IDEAS

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    1. Haas, Bénédicte & Rivero, Víctor, 2012. "Quasi-stationary distributions and Yaglom limits of self-similar Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 4054-4095.
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    Cited by:

    1. Leżaj, Łukasz, 2024. "Non-symmetric stable processes: Dirichlet heat kernel, Martin kernel and Yaglom limit," Stochastic Processes and their Applications, Elsevier, vol. 174(C).

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