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A note on the time-dependent and the stationary behaviour of a semi-infinite reservoir subject to a combination of Markovian inflows

Published online by Cambridge University Press:  14 July 2016

Emlyn H. Lloyd
Emlyn H. Lloyd*
Affiliation:
University of Lancaster
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Extract

The present theory of finite reservoirs is not rich in general theorems even when of the simple Moran type, with unit draft and stationary discrete independent-sequence inflows. For the corresponding systems with unbounded capacity however there are two classes of results which have been known for some time. One of these classes is concerned with the time-dependent solution, where the theory provides a functional equation for the generating function of the time to first emptiness (Kendall (1957)), and the other with the asymptotic stationary distribution of reservoir contents, for which an explicit formula for the generating function is available (Moran (1959)).

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971 , pp. 708 - 715
Copyright
Copyright © Applied Probability Trust 1971 

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References

Ali Khan, M. S. and Gani, J. (1968) Infinite dams with inputs forming a Markov chain. J. Appl. Prob. 5, 72–84.Google Scholar
Anis, A. A. and El-Naggar, A. S. T. (1968) The storage-stationary distribution in the case of two streams. J. Inst. Math. Appl. 4, 223–231.Google Scholar
Anis, A. A. and Lloyd, E H. (1972) Reservoirs with mixed Markovian and independent inflows. Siam J. Appl. Math. 22, No 1. (To appear).CrossRefGoogle Scholar
Gani, J. (1969) Recent advances in storage and flooding theory. Adv. Appl. Prob. 1, 73–110.Google Scholar
Kendall, D. G. (1957) Some problems in the theory of dams. J. R. Statist. Soc. B 19, 207–212.Google Scholar
Lloyd, E. H. (1963) Reservoirs with serially correlated inflows. Technometrics 5, 85–93.Google Scholar
Moran, P. A. P. (1959) The Theory of Storage. Methuen, London.Google Scholar
Odoom, S. and Lloyd, E. H. (1965) A note on the equilibrium distribution of levels in a semi-infinite reservoir subject to Markovian inputs and unit withdrawals. J. Appl. Prob. 2, 215–227.CrossRefGoogle Scholar