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

Zbigniew Palmowski*, Maria Vlasiou

*Corresponding author for this work

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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.
Original languageEnglish
Pages (from-to)153-167
Number of pages15
JournalQueueing systems
Volume96
Issue number1-2
Early online date10 Aug 2020
DOIs
Publication statusPublished - Oct 2020
Externally publishedYes

Keywords

  • Fluctuation theory
  • Laplace transforms
  • Lévy processes
  • Quasi-stationary distribution
  • Speed of convergence
  • Storage systems

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