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EXACT DISTRIBUTIONS IN A JUMP-DIFFUSION STORAGE MODEL

Published online by Cambridge University Press:  11 January 2002

David Perry  and
Wolfgang Stadje
David Perry
Affiliation:
University of Haifa, Haifa, Israel
Wolfgang Stadje
Affiliation:
University of Osnabrück, Osnabrück, Germany, E-mail: wolfgang@mathematik.uni-osnabrueck.de
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Abstract

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We consider a reflected independent superposition of a Brownian motion and a compound Poisson process with positive and negative jumps, which can be interpreted as a model for the content process of a storage system with different types of customers under heavy traffic. The distributions of the duration of a busy cycle and the maximum content during a cycle are determined in closed form.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 16 , Issue 1 , January 2002 , pp. 19 - 27
Copyright
© 2002 Cambridge University Press