Queues with Lévy input and hysteretic control

R. Bekker

doi:10.1007/s11134-009-9123-z

Queues with Lévy input and hysteretic control

R. Bekker

Mathematics

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Abstract

We consider a (doubly) reflected Lévy process where the Lévy exponent is controlled by a hysteretic policy consisting of two stages. In each stage there is typically a different service speed, drift parameter, or arrival rate. We determine the steady-state performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature, focusing on the special cases of M/G/1 queues and Brownian motion. © The Author(s) 2009.

Original language	English
Pages (from-to)	281-299
Number of pages	19
Journal	Queueing Systems
Volume	63
Issue number	1-4
DOIs	https://doi.org/10.1007/s11134-009-9123-z
Publication status	Published - 2009

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AB - We consider a (doubly) reflected Lévy process where the Lévy exponent is controlled by a hysteretic policy consisting of two stages. In each stage there is typically a different service speed, drift parameter, or arrival rate. We determine the steady-state performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature, focusing on the special cases of M/G/1 queues and Brownian motion. © The Author(s) 2009.

U2 - 10.1007/s11134-009-9123-z

DO - 10.1007/s11134-009-9123-z

M3 - Article

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VL - 63

SP - 281

EP - 299

JO - Queueing Systems

JF - Queueing Systems

IS - 1-4

ER -

Queues with Lévy input and hysteretic control

Abstract

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