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Recent advances in storage and flooding theory

Published online by Cambridge University Press:  01 July 2016

J. Gani
J. Gani*
Affiliation:
University of Sheffield
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Extract

The theory of storage processes, originally formulated by Moran [1] in 1954, has developed in the past fourteen years into a minor subfield of Applied Probability, closely allied to queueing theory. While dam models with discrete inputs are analogous to queueing processes, the essentially continuous nature of water inflows has distinguished generalized storage processes from queues. Indeed, some of the most complex of storage problems have arisen in the case of continuous flows.

Type
Research Article
Information
Advances in Applied Probability , Volume 1 , Issue 1 , Spring 1969 , pp. 90 - 110
Copyright
Copyright © Applied Probability Trust 

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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] Hurst, H. E. (1951) Long-term storage capacity of reservoirs. Trans. Amer. Soc. Civil Engrs. 116, 770–799.Google Scholar
[3] Gould, B. W. (1961) Statistical methods for estimating the design capacity of dams. J. Inst. Engrs. Aust. 33, 405–416.Google Scholar
[4] Harris, R. A. (1965) Probability of reservoir yield failure using Moran's steady-state probability method and Gould's probability routing method. J. Inst. Water Engrs. 19, 302–328.Google Scholar
[5] Langbein, W. B. (1958) Queueing theory and water storage. Proc. Amer. Soc. Civil Engrs. J. Hydr. Div. 84, Paper 1811.Google Scholar
[6] Gani, J. (1957) Problems in the probability theory of storage systems. J. R. Statist. Soc. B19, 181–206.Google Scholar
[7] Moran, P. A. P. (1959) The Theory of Storage. Methuen, London.Google Scholar
[8] Prabhu, N. U. (1964) Time dependent results in storage theory. J. Appl. Prob. 1, 1–46.CrossRefGoogle Scholar
[9] Lloyd, E. H. (1967) Stochastic reservoir theory. Advances in Hydroscience. Vol. 4. Academic Press Inc., New York.Google Scholar
[10] Bhat, B. R. and Gani, J. (1965) On the independence of yearly water inputs in dams. Proc. Reservoir Yield Symp., Oxford Part II, D5.16–5.26. WRA, Medmenham, Marlow, Bucks, England.Google Scholar
[11] Lloyd, E. H. (1963) Reservoirs with serially correlated inflows. Technometrics 5, 85–93.Google Scholar
[12] Lloyd, E. H. (1963) A probability theory of reservoirs with serially correlated inputs. J. Hydrol. 1, 99–128.CrossRefGoogle Scholar
[13] Lloyd, E. H. (1965) Probability of emptiness I: A critical review of some probability methods in the simple reservoir design problem. Proc. Reservoir Yield Symp., Oxford Part I, Paper 5. WRA, Medmenham, Marlow, Bucks, England.Google Scholar
[14] 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, 215–222.CrossRefGoogle Scholar
[15] Ali Khan, M. S. and Gani, J. (1968) Infinite dams with inputs forming a Markov chain. J. Appl. Prob. 5, 72–84.CrossRefGoogle Scholar
[16] Gani, J. (1968) A note on the first emptiness of dams with Markovian inputs. Stanford U. Tech. Report (to appear in J. Math. Anal. Appl. 26, April 1969).Google Scholar
[17] Kendall, D. G. (1957) Some problems in the theory of dams. J. R. Statist. Soc. B19, 207–212.Google Scholar
[18] Gani, J. and Prabhu, N. U. (1959) The time-dependent solution for a storage model with Poisson input. J. Math. Mech. 8, 653–664.Google Scholar
[19] Ali Khan, M. S. (1967) Dams with Markovian Inputs. , University of Sheffield (unpublished).Google Scholar
[20] Weesakul, B. (1961) First emptiness in a finite dam. J. R. Statist. Soc. B23, 343–351.Google Scholar
[21] Weesakul, B. (1961) The random walk between a reflecting and an absorbing barrier. Ann. Math. Statist. 32, 765–769.Google Scholar
[22] Prabhu, N. U. (1965) Queues and Inventories. John Wiley, New York.Google Scholar
[23] Moran, P. A. P. (1957) The statistical treatment of flood flows, Trans. Amer. Geophys. Union 38, 519–523.Google Scholar
[24] 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
[25] Gani, J. (1965) Flooding models. Proc. Reservoir Yield Symp., Oxford Part I, Paper 4. WRA, Medmenham, Marlow, Bucks, England.Google Scholar
[26] Phatarfod, R. (1963) Application of methods in sequential analysis to dam theory. Ann. Math. Statist. 34, 1588–1592.Google Scholar
[27] Dvoretzky, A., Kiefer, J. and Wolfowitz, J. (1953) Sequential decision problems for processes with continuous time parameter testing hypotheses. Ann. Math. Statist. 24, 254–264.CrossRefGoogle Scholar
[28] Bellman, R. (1957) On a generalization of the fundamental identity of Wald. Proc. Camb. Phil. Soc. 53, 257–9.CrossRefGoogle Scholar
[29] Tweedie, M. C. K. (1960) Generalization of Wald's fundamental identity of sequential analysis to Markov chains. Proc. Camb. Phil. Soc. 56, 205–214.CrossRefGoogle Scholar
[30] Miller, H. D. (1962) Absorption probabilities for sums of random variables defined on a finite Markov chain. Proc. Camb. Phil. Soc. 58, 286–298.CrossRefGoogle Scholar
[31] Phatarfod, R. M. (1965) Sequential analysis of dependent observations. Biometrika 52, 157–165.CrossRefGoogle Scholar
[32] Moran, P. A. P. (1967) Dams in series with continuous release. J. Appl. Prob. 4, 380–388.Google Scholar
[33] Takács, L. (1967) The distribution of the content of finite dams. J. Appl. Prob. 4, 151–161.CrossRefGoogle Scholar
[34] Bather, J. (1968) A diffusion model for the control of a dam. J. Appl. Prob. 5, 55–71.Google Scholar