A finite dam with variable release rate

Author:

Yeo G. F.

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).

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Cited by 20 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Dam Theory;Wiley StatsRef: Statistics Reference Online;2014-09-29

2. A New Look at Urban Water Storage in a Series of Connected Dams;Journal of Applied Probability;2014-03

3. A New Look at Urban Water Storage in a Series of Connected Dams;Journal of Applied Probability;2014-03

4. Modelling systems of reservoirs using structured Markov chains;Proceedings of the Institution of Civil Engineers - Water Management;2010-09

5. Optimal stormwater management with two dams: the dynamics of the pump–to–fill policy†;Optimization;2009-02

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