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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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References

[1] Blumenthal, R. and Getoor, R. K. (1968) Markov Processes and Potential Theory. Academic Press, New York.Google Scholar
[2] Çinlar, E. (1975) Introduction To Stochastic Processes. Prentice-Hall, Engelwood Cliffs N.J.Google Scholar
[3] Cohen, J. W. and Rubinovitch, M. (1977) On level crossings and cycles in dam processes. Math. Operat. Res. 2, 297–310.Google Scholar
[4] Cohen, J. W. (1982) The Single Server Queue, Revised Edition. North-Holland, Amsterdam.Google Scholar
[5] Davis, M. H. A. (1984) Piecewise deterministic Markov processes: a general class of non diffusion stochastic models. J. R. Statist. Soc. B 46, 353–388.Google Scholar
[6] Harrison, M. J. and Resnick, S. I. (1978) The recurrence classification of risk and storage processes. Math. Operat. Res. 3, 57–66.Google Scholar
[7] Kaspi, H. (1984) Storage processes with Markov additive input and output. Math. Operat. Res. 9, 424–440.Google Scholar
[8] Perry, D. and Levikson, B. (1989) Continuous production inventory model with analogy to certain queueing and dam models. Adv. Appl. Prob. 21, 123–141.CrossRefGoogle Scholar
[9] Prabhu, N. U. (1964) Queues and Inventories. Wiley, New York.Google Scholar