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Some exact results for dams with Markovian inputs

Published online by Cambridge University Press:  14 July 2016

Pyke Tin  and
R. M. Phatarfod
Pyke Tin
Affiliation:
Monash University, Clayton, Victoria
R. M. Phatarfod
Affiliation:
Monash University, Clayton, Victoria
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Abstract

In the theory of dams with Markovian inputs explicit results are not usually obtained, as the theory depends very heavily on the largest eigenvalue of the matrix (pijzj) where pij are the transition probabilities of the input process. In this paper we show that explicit results can be obtained if one considers an input process of a special form. The probability distribution of the time to first emptiness is obtained for both the finite and the infinite dam, as well as the stationary distribution of the dam content for the finite dam. Explicit results are given for the case where the stationary distribution of the input process has a geometric distribution.

Keywords

DAMSMARKOVIAN INPUTSFIRST EMPTINESSSTATIONARY DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 329 - 337
Copyright
Copyright © Applied Probability Trust 1976 

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References

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