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

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

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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.

Originele taal-2	Engels
Pagina's (van-tot)	153-167
Aantal pagina's	15
Tijdschrift	Queueing Systems
Volume	96
Nummer van het tijdschrift	1-2
Vroegere onlinedatum	10 aug 2020
DOI's	https://doi.org/10.1007/s11134-020-09664-w
Status	Gepubliceerd - 1 okt 2020

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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",

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KW - Fluctuation theory

KW - Laplace transforms

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

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