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

Zbigniew Palmowski (Corresponding author), Maria Vlasiou

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

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 - 1 Oct 2020

Funding

This work is partially supported by an NWO individual Grant through project 632.003.002 and by the National Science Centre under the grant 2018/B/ST1/00756 (2019-2022).

FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek632.003.002
Narodowe Centrum Nauki2018/B/ST1/00756, 2019-2022

    Keywords

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

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