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Infinite dams with discrete additive inputs

Published online by Cambridge University Press:  14 July 2016

M. S. Ali Khan
M. S. Ali Khan*
Affiliation:
University of Riyadh, Saudi Arabia
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Abstract

This paper considers an infinite dam fed by a discrete input Xt during the time interval [t, t + 1), t = 0, 1, 2, ···. At time t – 0 there is an output Yt = min(Zt–1, + Xt–1, r) from the dam leaving behind the amount Zt = max(0, Zt–1, + Xt–1, r). The probability Pr(Zt = i), i = 0, 1, 2, ··· is discussed under the strict assumption that r > 1 and the given initial condition that Z0 = u, u = 1, 2, ···. The generating function technique has been used throughout the paper.

Keywords

INFINITE DAMADDITIVE INPUTGENERATING FUNCTIONCHARACTERISTIC EQUATIONCHARACTERISTIC ROOTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 1 , March 1977 , pp. 170 - 180
Copyright
Copyright © Applied Probability Trust 1977 

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References

Ali Khan, M. S. (1976) Infinite dams with geometric inputs. Proceedings of the International Conference on Statistics, Computer Science and Social Research, Cairo, 5–8 April 1976, 73, 1–81.1.Google Scholar
Ali Khan, M. S. and Gani, J. (1968) Infinite dams with inputs forming a Markov chain. J. Appl. Prob. 5, 72–83.CrossRefGoogle Scholar
Brauer, A. (1962) On the theorems of Perron and Frobenius on non-negative matrices. In Studies in Mathematical Analysis and Related Topics, ed. Gilbarg, D., Solomon, H. et al., Stanford University Press, 48–55.Google Scholar
Brauer, A. (1964) On the characteristic roots of non-negative matrices. In Recent Advances in Matrix Theory, ed. Schneider, H., University of Wisconsin Press, Madison, 3–38.Google Scholar
Gani, J. (1958) Elementary methods in an occupancy problem of storage. Math. Ann. 136, 454–465.CrossRefGoogle Scholar
Gani, J. (1969) Recent advances in storage and flooding theory. Adv. Appl. Prob. 1, 90–110.CrossRefGoogle Scholar
Moran, P. A. P. (1954) A probability theory of dams and storage systems. Austral. J. Appl. Sci. 5, 116–124.Google Scholar
Prabhu, N. U. (1964) Time-dependent results in storage theory. J. Appl. Prob. 1, 1–46.CrossRefGoogle Scholar
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