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A storage model with continuous infinitely divisible inputs

  • J. Gani† (a1) and N. U. Prabhu (a2)

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).

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(2)Bene–, V. E.Theory of queues with one server. Trans. American Math. Soc. 94 (1960), 282294.
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(4)Doob, J. L.Stochastic processes (Wiley; New York, 1953).
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(7)Gani, J. and Pyke, R.The content of a dam as the supremum of an infinitely divisible process. J. Math. Mech. 9 (1960), 639652.
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(10)Kendall, D. G.Some problems in the theory of dams. J. Roy. Statist. Soc. Ser. B, 19 (1957), 207212.
(11)Lévy, P.Processus stochastiques et mouvement brownien (Gauthier-Villars; Paris, 1948).
(12)Meisling, T.Discrete-time queueing theory. Operations Res. 6 (1958), 96105.
(13)Moran, P. A. P.A probability theory of a dam with a continuous release. Quart. J. Math. Oxford Ser. (2), 7 (1956), 130137.
(14)Reich, E.Some combinatorial theorems for continuous time parameter processes. Math. Scand. 9 (1961), 243257.
(15)Tak´cs, L.Investigation of waiting time problems by reduction to Markov processes. Acta Math. Acad. Sci. Hungar. 6 (1955), 101129.

A storage model with continuous infinitely divisible inputs

  • J. Gani† (a1) and N. U. Prabhu (a2)

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