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

Zbigniew Palmowski; Maria Vlasiou

doi:10.1007/s11134-020-09664-w

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

Zbigniew Palmowski (Corresponding author), Maria Vlasiou

Stochastic Operations Research

Research output: Contribution to journal › Article › Academic › peer-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 language	English
Pages (from-to)	153-167
Number of pages	15
Journal	Queueing Systems
Volume	96
Issue number	1-2
Early online date	10 Aug 2020
DOIs	https://doi.org/10.1007/s11134-020-09664-w
Publication status	Published - 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).

Funders	Funder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	632.003.002
Narodowe Centrum Nauki	2018/B/ST1/00756, 2019-2022

Keywords

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

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10.1007/s11134-020-09664-w

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title = "Speed of convergence to the quasi-stationary distribution for L{\'e}vy input fluid queues",

abstract = "In this note, we prove that the speed of convergence of the workload of a L{\'e}vy-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.",

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KW - Lévy processes

KW - Quasi-stationary distribution

KW - Speed of convergence

KW - Storage systems

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

Abstract

Funding

Keywords

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A Lévy input fluid queue with input and workload regulation

A Lévy input fluid queue with input and workload regulation

A Lévy input model with additional state-dependent services

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