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A finite dam with exponential release

Published online by Cambridge University Press:  14 July 2016

G. F. Yeo
G. F. Yeo*
Affiliation:
University of Melbourne
*
* The author is currently at Linköping University, Sweden.
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Abstract

This paper considers a finite dam with independently and identically distributed (i.i.d.) inputs occurring in a Poisson process; the special cases where the inputs are (i) deterministic and (ii) negative exponentially distributed are considered in detail. The instantaneous release trate is proportional to the content, i.e., there is an exponential fall in conten except when inputs occur. This model may arise in several other situations such as a geiger counter or integrated shot noise. The distribution of the number of inputs, and of the time, to first overflowing is obtained in terms of generating functions; in Case (i) the solution is obtained through recurrence relations involving iterated integrals which can be evaluated numerically, and in Case (ii) using a series solution of a second order differential equation. Numerical results, in particular for the first two moments, are obtained for various values of the parameters of the model, and compared with a large number of simulations. Some remarks are also made about the infinite dam.

Keywords

FINITE DAMSPOISSON INPUTSEXPONENTIAL RELEASEFIRST PASSAGE TIMESRECURRENCE RELATIONSNUMERICAL INTEGRATIONSERIES SOLUTIONSIMULATION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 122 - 133
Copyright
Copyright © Applied Probability Trust 1974 

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References

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