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On infinite dams with inputs forming a stationary process

Published online by Cambridge University Press:  14 July 2016

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

This paper considers a dam of infinite capacity with a discrete-valued stationary input process and a unit release whenever possible. It is shown how, by suitable manipulations of the equation governing the dam content process, the stationary distribution of the dam being empty can be obtained, as also can (with a few additional assumptions) the expected value of the dam content in the stationary case. Results obtained are applied to particular cases of input — independent and identical, Markov, Bivariate Markov and moving-average.

Keywords

INFINITE DAMSSTATIONARY INPUTUNIT RELEASEEMPTINESS PROBABILITYEXPECTED DAM CONTENT
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974 , pp. 553 - 561
Copyright
Copyright © Applied Probability Trust 1974 

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