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Tail Asymptotics for a Random Sign Lindley Recursion

Part of: Limit theorems Special processes

Published online by Cambridge University Press:  14 July 2016

Maria Vlasiou  and
Zbigniew Palmowski
Maria Vlasiou*
Affiliation:
Eindhoven University of Technology
Zbigniew Palmowski*
Affiliation:
University of Wrocław
*
∗Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands. Email address: m.vlasiou@tue.nl
∗∗Postal address: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland. Email address: zpalma@math.uni.wroc.pl
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Abstract

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We investigate the tail behaviour of the steady-state distribution of a stochastic recursion that generalises Lindley's recursion. This recursion arises in queueing systems with dependent interarrival and service times, and includes alternating service systems and carousel storage systems as special cases. We obtain precise tail asymptotics in three qualitatively different cases, and compare these with existing results for Lindley's recursion and for alternating service systems.

Keywords

Stochastic recursionCramér conditionssubexponential distributionintermediate tailsharp asymptotics

MSC classification

Secondary: 60F10: Large deviations 60K25: Queueing theory
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 72 - 83
Copyright
Copyright © Applied Probability Trust 2010 

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