Finite dams with inputs forming a Markov chain
- 1 April 1970
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 7 (02) , 291-303
- https://doi.org/10.1017/s0021900200034884
Abstract
This paper considers a finite dam fed by inputs forming a Markov chain. Relations for the probability of first emptiness before overflow and with overflow are obtained and their probability generating functions are derived; expressions are obtained in the case of a three state transition probability matrix. An equation for the probability that the dam ever dries up before overflow is derived and it is shown that the ratio of these probabilities is independent of the size of the dam. A time dependent formula for the probability distribution of the dam content is also obtained.Keywords
This publication has 5 references indexed in Scilit:
- Infinite dams with inputs forming a Markov chainJournal of Applied Probability, 1968
- A note on the equilibrium distribution of levels in a semi-infinite reservoir subject to Markovian inputs and unit withdrawalsJournal of Applied Probability, 1965
- A Convexity Property in the Theory of Random Variables Defined on a Finite Markov ChainThe Annals of Mathematical Statistics, 1961
- Emptiness in the Finite DamThe Annals of Mathematical Statistics, 1960
- Some Exact Results for the Finite DamThe Annals of Mathematical Statistics, 1958