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Dams with autoregressive inputs

Published online by Cambridge University Press:  14 July 2016

P. S. Collings
P. S. Collings*
Affiliation:
University of Sheffield
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Abstract

In this paper a dam with autoregressive inputs and unit outputs is considered. Approximations for the distributions of the times to first emptiness and overflow are obtained using a Wald-type identity. The limiting behaviour of the dam content is also investigated

Keywords

DAMSFIRST EMPTINESSAUTOREGRESSIVE PROCESSESWALD'S IDENTITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 533 - 541
Copyright
Copyright © Applied Probability Trust 1975 

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References

Arjas, E. (1972) On a fundamental identity in the theory of semi-Markov processes. Adv. Appl. Prob. 4, 258–270.Google Scholar
Bhat, B. R. and Gani, J. (1968) The independence of yearly water inputs in dams. Proc. 1965 Reservoir Yield Symposium, Oxford, Part II (1968) D5.16–D5.26.Google Scholar
Lloyd, E. H. (1963) Reservoir with serially correlated input. Technometrics 5, 85–93.Google Scholar
Loynes, R. M. (1962) The stability of a queue with non-independent interarrival and service times. Proc. Camb. Phil. Soc. 58, 497–520.CrossRefGoogle Scholar
Matthews, J. P. (1971) A study of processes associated with a finite Markov chain. Ph.D. thesis, University of Sheffield.Google Scholar
Moran, P. A. P. (1954) A probability theory of dams and storage systems. Austral. J. Appl. Sci. 5, 116–124.Google Scholar
Neveu, J. (1975) Discrte-Parameter Martingales. North-Holland, Amsterdam and New York.Google Scholar
Pakes, A. G. (1973) On dams with Markovian inputs. J. Appl Prob. 10, 317–329.CrossRefGoogle Scholar
Phatarfod, R. M. (1971) Some approximate results in renewal and dam theories. J. Austral. Math. Soc. 12, 425–432.Google Scholar
Roesner, L. A. and Yevdjevich, V. M. (1966) Mathematical models for time series of monthly precipitation and monthly run-off. Hydrology papers No. 15, Colorado State University.Google Scholar
Tin, P. and Phatarfod, R. M. (1974) On infinite dams with inputs forming a stationary process. J. Appl. Prob. 11, 553–561.CrossRefGoogle Scholar
Turnbull, B. W. (1972) Chebyshev-like inequalities for dam models. J. Appl. Prob. 9, 617–629.CrossRefGoogle Scholar