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A storage model with continuous infinitely divisible inputs

Published online by Cambridge University Press:  24 October 2008

J. Gani†  and
N. U. Prabhu
J. Gani†
Affiliation:
Australian National University
N. U. Prabhu
Affiliation:
University of Western Australia
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Abstract

This paper presents a general theory of storage for dams subject to a steady release, and with continuous inputs having infinitely divisible distributions. The paper extends some earlier work by Downton, Lindley, Smith and Kendall ((10), see discussion), and gives a detailed account of results previously sketched by the authors (6).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 417 - 430
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Beneš, V. E.On queues with Poisson arrivals. Ann. Math. Statist. 28 (1957), 670–677.CrossRefGoogle Scholar
(2)Bene–, V. E.Theory of queues with one server. Trans. American Math. Soc. 94 (1960), 282–294.CrossRefGoogle Scholar
(3)Darling, D. A. and Siegert, A. J. F., The first passage problem for a continuous Markov process. Ann. Math. Statist. 24 (1953), 624–639.CrossRefGoogle Scholar
(4)Doob, J. L.Stochastic processes (Wiley; New York, 1953).Google Scholar
(5)Downton, F.A note on Moran's theory of dams. Quart. J. Math. Oxford Ser. (2), 8 (1957), 282–286.CrossRefGoogle Scholar
(6)Gani, J. and Prabhu, N. U., Remarks on the dam with Poisson type inputs. Aust. J. Appl. Sci. 10 (1959), 113–122.Google Scholar
(7)Gani, J. and Pyke, R.The content of a dam as the supremum of an infinitely divisible process. J. Math. Mech. 9 (1960), 639–652.Google Scholar
(8)Gnedenko, B. V. and Kolmogorov, A. N.Limit distributions for sums of independent random variables (Addison-Wesley; Cambridge, Mass., 1954).Google Scholar
(9)Kendall, D. G.Some problems in the theory of queues. J. Roy. Statist. Soc. Ser. B, 13 (1951), 151–173.Google Scholar
(10)Kendall, D. G.Some problems in the theory of dams. J. Roy. Statist. Soc. Ser. B, 19 (1957), 207–212.Google Scholar
(11)Lévy, P.Processus stochastiques et mouvement brownien (Gauthier-Villars; Paris, 1948).Google Scholar
(12)Meisling, T.Discrete-time queueing theory. Operations Res. 6 (1958), 96–105.CrossRefGoogle Scholar
(13)Moran, P. A. P.A probability theory of a dam with a continuous release. Quart. J. Math. Oxford Ser. (2), 7 (1956), 130–137.CrossRefGoogle Scholar
(14)Reich, E.Some combinatorial theorems for continuous time parameter processes. Math. Scand. 9 (1961), 243–257.CrossRefGoogle Scholar
(15)Tak´cs, L.Investigation of waiting time problems by reduction to Markov processes. Acta Math. Acad. Sci. Hungar. 6 (1955), 101–129.CrossRefGoogle Scholar