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The busy cycle of the reflected superposition of Brownian motion and a compound Poisson process

Part of: Markov processes Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

David Perry  and
Wolfgang Stadje
David Perry*
Affiliation:
University of Haifa
Wolfgang Stadje*
Affiliation:
Universität Osnabrück
*
∗ Postal address: University of Haifa, Department of Statistics, Haifa 31905, Israel.
∗∗ Postal address: Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany. Email address: [email protected]
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Abstract

We consider a reflected superposition of a Brownian motion and a compound Poisson process as a model for the workload process of a queueing system with two types of customers under heavy traffic. The distributions of the duration of a busy cycle and the maximum workload during a cycle are determined in closed form.

Keywords

Brownian motioncompound Poisson processreflectionqueueingworkloadheavy trafficbusy cyclemaximum

MSC classification

Primary: 60K25: Queueing theory 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 60G51: Processes with independent increments; L'evy processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 1 , March 2001 , pp. 255 - 261
Copyright
Copyright © by the Applied Probability Trust 2001 

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