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

Shirley Odoom · Emlyn H. Lloyd

42 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

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.

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1969Recent advances in storage and flooding theory 1973Some results for dams with Markovian inputs 1975Combinatorial and analytic methods in the theory of queues 1972A storage model in which the net growth-rate is a Markov chain 1972A simple model for a dam in continuous time with Markovian input 1972An infinite discrete dam with dependent inputs 1971A note on the first emptiness time of an infinite reservoir with inputs forming a Markov chain 1975Combinatorial and analytic methods in the theory of queues

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