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Dams with additive inputs revisited

Published online by Cambridge University Press:  14 July 2016

P. A. Pegg  and
R. M. Phatarfod
P. A. Pegg
Affiliation:
Polytechnic of North London
R. M. Phatarfod
Affiliation:
Monash University, Clayton, Victoria
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Abstract

In this paper we consider a finite dam with unit release. Ratio identities are derived for the various random walks involved, and from them are derived the p.g.f. of the time of first emptiness with and without overflow and the complete time-dependent distribution of the dam content.

Keywords

FINITE DAMUNIT RELEASERATIO IDENTITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 367 - 374
Copyright
Copyright © Applied Probability Trust 1977 

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References

[1] Prabhu, N. U. (1964) Time-dependent results in storage theory J. Appl. Prob. 1, 1–46.Google Scholar
[2] Prabhu, N. U. (1965) Queues and Inventories. Wiley, New York.Google Scholar
[3] Roes, P. B. ?. (1972) The finite dam with discrete additive input. J. Engineering Maths. 6, 37–45.Google Scholar
[4] Phatarfod, R. M., Speed, T. P. and Walker, A. M. (1971) A note on random walk. J. Appl. Prob. 8, 198–201.CrossRefGoogle Scholar
[5] Pegg, P. A. (1973) Some ratio identities for a class of skip-free random walks. J. Appl. Prob. 213–217.Google Scholar
[6] 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