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^*, Maria Vlasiou

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

2 Citations (Scopus)

39 Downloads (Pure)

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 - Oct 2020
Externally published	Yes

Keywords

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

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10.1007/s11134-020-09664-wLicence: CC BY

ArticleFinal published version, 319 KBLicence: CC BY

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Cite this

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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.",

keywords = "Fluctuation theory, Laplace transforms, L{\'e}vy processes, Quasi-stationary distribution, Speed of convergence, Storage systems",

author = "Zbigniew Palmowski and Maria Vlasiou",

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T1 - Speed of convergence to the quasi-stationary distribution for Lévy input fluid queues

AU - Palmowski, Zbigniew

AU - Vlasiou, Maria

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N2 - 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.

AB - 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.

KW - Fluctuation theory

KW - Laplace transforms

KW - Lévy processes

KW - Quasi-stationary distribution

KW - Speed of convergence

KW - Storage systems

U2 - 10.1007/s11134-020-09664-w

DO - 10.1007/s11134-020-09664-w

M3 - Article

SN - 0257-0130

VL - 96

SP - 153

EP - 167

JO - Queueing systems

JF - Queueing systems

IS - 1-2

ER -

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

Abstract

Keywords

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