An infinite depth dam with Poisson input and Poisson release |
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| Authors: | Prem S Puri Jerome N Senturia |
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| Institution: | 1. Purdue University , Indiana , W. Lafayette , USA;2. University of Wisconsin , Wisconsin , Madison , USA |
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| Abstract: | Abstract In this paper the content Z(t) of a dam where Z(t) ε( - ∞, h], h an arbitrary constant, is studied. Inputs to the dam form a sequence of i.i.d. r.v.'s and occur according to a Poisson process with parameter λ > 0 while releases from the dam form a sequence of i.i.d. r.v.'s and occur according to a Poisson process with parameter μ > 0. The Laplace transform of the process Z(t) is derived and expressions for the moments are given. It is shown that Z(t) has a nondegenerate limiting distribution, as t -- ∞, if average inputs per unit time exceed average releases per unit time. |
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