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On the limit behavior of certain quantities in a subcritical storage model

Published online by Cambridge University Press:  01 July 2016

Prem S. Puri  and
Eric S. Tollar
Prem S. Puri*
Affiliation:
Purdue University
Eric S. Tollar*
Affiliation:
The Florida State University
*
∗Postal address: Department of Statistics, Purdue University, West Lafayette, IN 47907, USA.
†Postal address: Department of Statistics, The Florida State University, Tallahassee, FL 32306, USA.
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Abstract

The limit behavior of the content of a subcriticai storage model defined on a semi-Markov process is examined. This is achieved by creating a renewal equation using a regeneration point (i0,0) of the process. By showing that the expected return time to (i0, 0) is finite, the conditions needed for the basic renewal theorem are established. The joint asymptotic distribution of the content of the storage at time t and the accumulated amount of the unmet (lost) demands during (0,t) is then established by showing the asymptotic independence of these two.

Keywords

TOTAL DEMAND LOSTMARKOV CHAINSSEMI-MARKOV PROCESSESΦ-IRREDUCIBILITYERGODICITYRENEWAL THEORYSTORAGE LEVEL
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 2 , June 1985 , pp. 443 - 459
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Research carried out while the second author was a David Ross Fellow of Purdue University.

These investigations were supported in part by U.S. National Science Foundation Grant No. MCS-8102733.

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