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On a duality between a non-Markoyian storage/production process and a Markovian dam process with state-dependent input and output

Published online by Cambridge University Press:  14 July 2016

Haya Kaspi  and
David Perry
Haya Kaspi*
Affiliation:
Technion — Israel Institute of Technology
David Perry*
Affiliation:
University of Haifa
*
∗ Postal address: Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology, Haifa, Israel.
∗∗ Postal address: Department of Statistics, The University of Haifa, Haifa, Israel.
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Abstract

We consider a storage/production process where the production rate is state dependent, the demand arrival is a renewal process, and the sizes of the demands are i.i.d exponentially distributed random variables. The resulting content process is non-Markovian but regenerative. We construct a dual Markovian dam process with drift, jump rate and jump sizes that are state dependent and use it to compute the limiting one-dimensional distribution of the content process.

Keywords

LEVEL CROSSINGPIECEWISE DETERMINISTIC PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 835 - 844
Copyright
Copyright © Applied Probability Trust 1989 

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