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A note on the equilibrium distribution of levels in a semi-infinite reservoir subject to Markovian inputs and unit withdrawals

Published online by Cambridge University Press:  14 July 2016

S. Odoom  and
E. H. Lloyd
S. Odoom
Affiliation:
University of Ghana
E. H. Lloyd
Affiliation:
University of Lancaster
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Extract

A well-known theorem (Moran, 1959) relating to the equilibrium condition of a semi-infinite “Moran reservoir” with stationary independent inputs and unit output, gives (a) the probability of emptiness, and (b) the generating function of the distribution of levels, in terms of the input distribution. A further theorem (Prabhu, 1958) points out that, in a finite reservoir, the ratio of the probabilities of any two comparable levels is independent of the size of the reservoir, and and is in fact the same as the corresponding ratio for the semi-infinite reservoir. In the present note the theorems are extended to deal with the case of Markovian inputs.

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 1 , June 1965 , pp. 215 - 222
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

Lloyd, E. H. (1963) Reservoirs with serially correlated inflows. Technometrics 5, 85–93.Google Scholar
Lloyd, E. H. and Odoom, S. (1964) A note on the solution of dam equations. To appear in J. R. Statist. Soc. B.Google Scholar
Moran, P. A. P. (1959) The Theory of Storage. Methuen, London.Google Scholar
Prabhu, N. U. (1958) Some exact results for the finite dam. Ann. Math. Statist. 29, 1234–1243.Google Scholar