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A finite dam with variable release rate

Published online by Cambridge University Press:  14 July 2016

G. F. Yeo
G. F. Yeo*
Affiliation:
University of Melbourne
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Abstract

This note considers a finite dam fed by independently and identically distributed (i.i.d.) inputs, being either (i) of at least size β (> 0) or (ii) negative exponentially distributed, occurring in a Poisson process. The instantaneous release rate may be a function r(·) of the content; additional and numerical results are given for the special case where r(x) = µxα (0 ≦ α<∞, 0 < µ <∞) is proportional to the αth power of the content. The basic method used in [7] for the special case r(x) = µx for obtaining the distribution of the number of steps and of the time to first overflowing is shown to carry over almost completely in case (i), but only partially so in case (ii).

Keywords

FINITE DAMCOMPOUND POISSON INPUTSRECURRENCE RELATIONSNUMERICAL INTEGRATIONORDINARY DIFFERENTIAL EQUATIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 205 - 211
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Çinlar, E. and Pinsky, M. (1972) On dams with additive inputs and a general release rule. J. Appl. Prob. 9, 422–429.Google Scholar
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[3] Mcneil, D. R. (1972) A simple model for a dam in continuous time with Markovian inputs. Z. Wahrscheinlichkeitsth. Geb. 21, 241–254.Google Scholar
[4] Moran, P. A. P. (1969) A theory of dams with continuous input and a general release rule. J. Appl. Prob. 6, 88–98.Google Scholar
[5] Murphy, G. M. (1960) Ordinary Differential Equations and Their Solutions . Van Nostrand.Google Scholar
[6] Saaty, T. M. (1961) Elements of Queueing Theory. McGraw-Hill.Google Scholar
[7] Yeo, G. F. (1974) A finite dam with exponential release. J. Appl. Prob. 11, 122–133.Google Scholar