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Some limit theorems for the general semi-Markov storage model

Published online by Cambridge University Press:  14 July 2016

K. Balagopal
K. Balagopal*
Affiliation:
Regional Engineering College, Warangal
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Abstract

In this paper we treat the general version of the semi-Markov storage model, introduced first by Senturia and Puri: transitions in the state of the system occur at a discrete sequence of time points, described by a two-state semi-Markov process. An input occurs at an instant of transition to state 1 and a demand for release occurs at an instant of transition to state 2.

Assuming general distributions for all the variables involved, we show that the dam contents just after the nth input converges properly in distribution as n →∞ under conditions of stability; likewise that after the nth demand. We also show that the demand lost due to shortage of stock, accumulated over instants of demand as well as over time, obeys a strong law and a central limit theorem.

Keywords

STORAGE SYSTEMCONTENTS AFTER INPUTDEMANDDEMAND LOSTMARKOV RENEWAL THEORYLIMITS IN DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 3 , September 1979 , pp. 607 - 617
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

∗

Present address: Statistical Quality Control and Operations Research Unit, Indian Statistical Institute, 7, S. J. S. Sansanwal Marg, New Delhi 110 029, India.

References

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