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Loss rate for a general Lévy process with downward periodic barrier

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Zbigniew Palmowski  and
Przemysław Świa̧tek
Zbigniew Palmowski
Affiliation:
University of Wrocław, Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland. Email address: zbigniew.palmowski@math.uni.wroc.pl
Przemysław Świa̧tek
Affiliation:
University of Wrocław, Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland. Email address: przemyslaw.swiatek@math.uni.wroc.pl
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Abstract

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In this paper we consider a general Lévy process X reflected at a downward periodic barrier At and a constant upper barrier K, giving a process VKt=Xt +LAt−LKt. We find the expression for a loss rate defined by lK=ELK1 and identify its asymptotics as K→∞ when X has light-tailed jumps and EX1<0.

Keywords

Loss rateLévy processbarrierqueueing process

MSC classification

Primary: 60K05: Renewal theory 60K25: Queueing theory
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Part 2. Lévy Processes
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 99 - 108
Copyright
Copyright © Applied Probability Trust 2011 

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