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On dams of finite capacity

Published online by Cambridge University Press:  09 April 2009

Lajos Takács
Lajos Takács
Affiliation:
Department of MathematicsCase Western Reserve UniversityCleveland, Ohio, U.S.A.
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We shall consider the following mathematical model of dams of finite capacity. In the time interval (0, ∞) water is flowing into a dam (reservoir). Denote by χ(u) the total quantity of water flowing into the dam in the time interval (0, u). The capacity of the dam is a finite positive number h. If the dam becomes full, the excess water overflows. Denote by δ(u) the total quantity of water demanded in the time interval (0, u). If there is enough water in the reservoir the demand is satisfied, if there is not enough water the difference is supplied from elsewhere Denote by η(t) the content of the dam at time t. η(0) is the initial content.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 2 , May 1968 , pp. 161 - 170
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Baxter, G. and Shapiro, J. M., ‘On bounded infinitely divisible random variables’, Sankhyā, 22 (1960), 253–260.Google Scholar
[2]Gani, J. and Prabhu, N. U., ‘Continuous time treatment of a storage problem’, Nature, 182 (1958), 39–40.Google Scholar
[3]Moran, P. A. P., ‘A probability theory of a dam with continuous release’, Quart. Journ. Math. Oxford, 7 (1956), 130–137.CrossRefGoogle Scholar
[4]Takács, L., Combinatorial Methods in the Theory of Stochastic Processes (John Wiley and Sons, New York, 1967).Google Scholar
[5]Weesakul, B. and Yeo, G., ‘Some problems in finite dams with an application to insurance risk’, Zeitschrift für Wahrscheinlichkeitstheorie 2 (1963), 135–146.Google Scholar