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

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

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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AU - Vlasiou, Maria

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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

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DO - 10.1007/s11134-020-09664-w

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IS - 1-2

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

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