Skip to main content Accessibility help
×
Home

Infinite dams with discrete additive inputs

  • M. S. Ali Khan (a1)

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 Z 0 = u, u = 1, 2, ···. The generating function technique has been used throughout the paper.

Copyright

References

Hide All
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.
Ali Khan, M. S. and Gani, J. (1968) Infinite dams with inputs forming a Markov chain. J. Appl. Prob. 5, 7283.
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, 4855.
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, 338.
Gani, J. (1958) Elementary methods in an occupancy problem of storage. Math. Ann. 136, 454465.
Gani, J. (1969) Recent advances in storage and flooding theory. Adv. Appl. Prob. 1, 90110.
Moran, P. A. P. (1954) A probability theory of dams and storage systems. Austral. J. Appl. Sci. 5, 116124.
Prabhu, N. U. (1964) Time-dependent results in storage theory. J. Appl. Prob. 1, 146.
Yeo, G. F. (1961) The time-dependent solution for an infinite dam with discrete additive inputs. J. R. Statist. Soc. B 23, 173179.

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed