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Dams in series with continuous release

Published online by Cambridge University Press:  14 July 2016

P.A.P. Moran
P.A.P. Moran*
Affiliation:
Australian National University
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Extract

In a previous paper (Moran (1956)) the theory of a dam with a continuous release was developed for a situation in which the input was defined by an additive homogeneous random process of gamma distribution type, and the release was defined to occur continuously at a fixed rate when the content of the dam was non-zero. In the present paper we modify these conditions by assuming first that the input is defined by a general additive homogeneous process with non-negative increments with finite second moment, and secondly that the rate of release is proportional to the content of the dam. This modification to the release rule ensures that the content of the dam is never zero and the theory is then so simplified that the distributional properties of the contents of a sequence of dams in series can be easily found.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 2 , August 1967 , pp. 380 - 388
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

Baxter, G. and Shapiro, J. M. (1960) On bounded infinitely divisible distributions. Sankhya 22, 253–260.Google Scholar
Doob, J. L. (1953) Stochastic Processes. J. Wiley, New York.Google Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications. Volume II. J. Wiley, New York.Google Scholar
Moran, P.A.P. (1956) A probability theory of a dam with a continuous release. Quart. J. Math. (2), 7, 130–137.CrossRefGoogle Scholar