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Infinite dams with inputs forming a Markov chain

Published online by Cambridge University Press:  14 July 2016

M. S. Ali Khan  and
J. Gani
J. Gani
Affiliation:
University of Sheffield
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Extract

Moran's [1] early investigations into the theory of storage systems began in 1954 with a paper on finite dams; the inputs flowing into these during consecutive annual time-intervals were assumed to form a sequence of independent and identically distributed random variables. Until 1963, storage theory concentrated essentially on an examination of dams, both finite and infinite, fed by inputs (discrete or continuous) which were additive. For reviews of the literature in this field up to 1963, the reader is referred to Gani [2] and Prabhu [3].

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 1 , April 1968 , pp. 72 - 83
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

5. References

[1] Moran, P. A. P. (1954) A probability theory of dams and storage systems. Aust. J. Appl. Sci. 5, 116–124.Google Scholar
[2] Gani, J. (1957) Problems in the probability theory of storage systems. J. R. Statist. Soc. B 19, 181–206.Google Scholar
[3] Prabhu, N. U. (1964) Time-dependent results in storage theory. J. Appl. Prob. 1, 1–46.CrossRefGoogle Scholar
[4] Lloyd, E. H. and Odoom, S. (1963) Reservoirs with correlated inflows. Technometrics 5, 85–93.Google Scholar
[5] Lloyd, E. H. and Odoom, S. (1964) A note on the solution of dam equations. J.R. Statist. Soc. B 26, 338–344.Google Scholar
[6] Lloyd, E. H. and Odoom, S. (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, 215–222.Google Scholar
[7] Yeo, G. F. (1961) The time-dependent solution for an infinite dam with discrete additive inputs. J.R.Statist. Soc. B 23, 173–179.Google Scholar
[8] Volkov, I. S. (1958) On the distribution of sums of random variables defined on a homogeneous Markov chain with a finite number of states. Th.Prob.Appl. 3, 384–399.CrossRefGoogle Scholar
[9] Miller, H. D. (1961) A convexity property in the theory of random variables defined on a finite Markov chain. Ann. Math. Statist. 32, 1260–1270.CrossRefGoogle Scholar
[10] Miller, H. D. (1962) A matrix factorization problem in the theory of random variables defined on a finite Markov chain. Proc. Camb. Phil. Soc. 58, 268–285.Google Scholar
[11] Gani, J. (1958) Elementary methods for an occupancy problem of storage. Math. Ann. 136, 454–465.Google Scholar
[12] Phatarfod, R. M. (1965) A note on cumulative sums of Markovian variables. J. Aust.Math. Soc. 5, 285–287.CrossRefGoogle Scholar
[13] Ali Khan, M. S. (1967) Dams with Markovian Inputs. Ph.D. Thesis, University of Sheffield.Google Scholar