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Some new results in storage theory

Published online by Cambridge University Press:  14 July 2016

N. U. Prabhu*
Affiliation:
Cornell University

Extract

In the storage model proposed by Kendall [6], the input is assumed to be a stochastic process with stationary independent increments, and the release is continuous and is at a unit rate. The storage process arising from this model is known to reach a steady state if the expected net input per unit time is negative. In this paper we consider the situation where this expected net input is nonnegative and derive limiting distributions for the wet period, total dry period during a given time interval and the dam content.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1968 

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References

[1] Beneš, V. E. (1957) On queues with Poisson arrivals. Ann. Math. Statist. 28, 670677.CrossRefGoogle Scholar
[2] Brody, S. M. (1963) On a limiting theorem of the theory of queues. Ukrain. Mat. Z. 15, 7679.Google Scholar
[3] Darling, D. A. and Kac, M. (1957) On occupation times for Markov processes. Trans. Amer. Math. Soc. 84, 444458.CrossRefGoogle Scholar
[4] Feller, W. (1966) An Introduction to Probability Theory and Its Applications. Vol. II. John Wiley, New York.Google Scholar
[5] Gani, J. and Prabhu, N. U. (1963) A storage model with continuous infinitely divisible inputs. Proc. Camb. Phil. Soc. 59, 417429.Google Scholar
[6] Kendall, D. G. (1957) Some problems in the theory of dams. J.R. Statist. Soc. B 19, 207212.Google Scholar
[7] Prabhu, N. U. (1965) Queues and Inventories. John Wiley, New York.Google Scholar