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On infinite dams with inputs forming a stationary process

Published online by Cambridge University Press:  14 July 2016

Pyke Tin  and
R. M. Phatarfod
Pyke Tin
Affiliation:
Monash University
R. M. Phatarfod
Affiliation:
Monash University
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Abstract

This paper considers a dam of infinite capacity with a discrete-valued stationary input process and a unit release whenever possible. It is shown how, by suitable manipulations of the equation governing the dam content process, the stationary distribution of the dam being empty can be obtained, as also can (with a few additional assumptions) the expected value of the dam content in the stationary case. Results obtained are applied to particular cases of input — independent and identical, Markov, Bivariate Markov and moving-average.

Keywords

INFINITE DAMSSTATIONARY INPUTUNIT RELEASEEMPTINESS PROBABILITYEXPECTED DAM CONTENT
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974 , pp. 553 - 561
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Moran, P. A. P. (1954) A probability theory of dams and storage systems. Austral. J. Appl. Sci. 5, 116–124.Google Scholar
[2] Prabhu, N. U. (1958) Some exact results for the finite dam. Ann. Math. Statist. 29, 1234–1243.CrossRefGoogle Scholar
[3] Yeo, G. F. (1961) The time-dependent solution for an infinite dam with discrete additive inputs. J. R. Statist. Soc. B 23, 173–179.Google Scholar
[4] Gani, J. (1957) Problems in the probability theory of storage. J. R. Statist. Soc. B 19, 181–206.Google Scholar
[5] Lloyd, E. (1963) Reservoirs with correlated inflows. Technometrics 5, 85–93.Google Scholar
[6] Odoom, S. and Lloyd, E. H. (1965) A note on the equilibrium distribution of levels in a semi-infinite reservoir subject to Markovian inputs and unit withdrawals. J. Appl. Prob. 2, 215–222.CrossRefGoogle Scholar
[7] Ali Khan, M. S. and Gani, J. (1968) Infinite dams with inputs forming a Markov chain. J. Appl. Prob. 5, 72–83.Google Scholar
[8] Brockwell, P. J. and Gani, J. (1970) A population process with Markovian progenies. J. Math. Anal. Appl. 32, 264–273.Google Scholar
[9] Phatarfod, R. M. and Mardia, K. V. (1973) Some results for dams with Markovian inputs. J. Appl. Prob. 10, 166–180.CrossRefGoogle Scholar
[10] Pakes, A. G. (1973) On dams with Markovian inputs. J. Appl. Prob. 10, 317–329.CrossRefGoogle Scholar
[11] Anis, A. A. and Lloyd, E. H. (1972) Reservoirs with mixed Markovian and independent inflows. Siam J. Appl. Math. 22, 68–76.CrossRefGoogle Scholar
[12] Lloyd, E. H. (1971) A note on the time-dependent and stationary behaviour of a semi-infinite reservoir subject to a combination of Markovian inflows. J. Appl. Prob. 8, 708–715.Google Scholar
[13] Herbert, H. G. (1972) An infinite discrete dam with dependent inputs. J. Appl. Prob. 9, 404–413.Google Scholar