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A theory of dams with continuous input and a general release rule

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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Abstract

Consider an infinite capacity dam in which the input and release occur continuously in time. Write X(t) for the total input up to time t starting from X(0) = 0 at t = 0. Let Z(t) be the content of the dam at time t and R(u) (0 ≦ u < ∞) a release function such that in any interval of time (t, t + dt), the amount of water released is R(Z(t))dt + o(t) for any bounded realisation of the process {Z(t)}. Thus R(u) can be regarded as a “rate of release”.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 1 , April 1969 , pp. 88 - 98
Copyright
Copyright © Applied Probability Trust 

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References

Gani, J. and Prabhu, N. U. (1963) A storage model with continuous infinitely divisible inputs. Proc. Camb. Phil. Soc. 59, 417–429.Google Scholar
Moran, P. A. P. (1956) A probability theory of a dam with a continuous release. Quart, J. Math. 7, 130–137.Google Scholar
Moran, P. A. P. (1967) Dams in series with continuous release. J. Appl. Prob. 4, 380–388.CrossRefGoogle Scholar
Moran, P. A. P. (1968) Introduction to Probability Theory, Oxford University Press.Google Scholar