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Finite dams with inputs forming a Markov chain

Published online by Cambridge University Press:  14 July 2016

M.S. Ali Khan
M.S. Ali Khan*
Affiliation:
Peshawar University
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Abstract

This paper considers a finite dam fed by inputs forming a Markov chain. Relations for the probability of first emptiness before overflow and with overflow are obtained and their probability generating functions are derived; expressions are obtained in the case of a three state transition probability matrix. An equation for the probability that the dam ever dries up before overflow is derived and it is shown that the ratio of these probabilities is independent of the size of the dam. A time dependent formula for the probability distribution of the dam content is also obtained.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 291 - 303
Copyright
Copyright © Applied Probability Trust 1970 

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References

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