A storage model in which the net growth-rate is a Markov chain

Peter J. Brockwell

13 citations0/0 files storedJournal of Applied Probability

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

Abstract

The distribution of the times to first emptiness and first overflow, together with the limiting distribution of content are determined for a dam of finite capacity. It is assumed that the rate of change of the level of the dam is a continuous-time Markov chain with finite state-space (suitably modified when the dam is full or empty).

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1970Finite dams with inputs forming a Markov chain 1968Infinite dams with inputs forming a Markov chain 1965A note on the equilibrium distribution of levels in a semi-infinite reservoir subject to Markovian inputs and unit withdrawals 1965Boundary problems for additive processes defined on a finite Markov chain

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1982The control of a finite dam

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