Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T20:16:13.769Z Has data issue: false hasContentIssue false
  • English
  • Français

An infinite discrete dam with dependent inputs

Published online by Cambridge University Press:  14 July 2016

H. G. Herbert
H. G. Herbert*
Affiliation:
University of Western Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is concerned with an infinite discrete dam fed by inputs which form a moving average sequence. Generating functions are derived for the joint time dependent distribution of the content, accumulated input and total dry time, the distribution of first emptiness, and the stationary content distribution. Also investigated is the problem of first emptiness before overflow for the finite dam.

Keywords

TRANSIENT BEHAVIOURSTATIONARY BEHAVIOURFIRST EMPTINESSINFINITE DISCRETE DAM MOVING AVERAGE INPUT
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 404 - 413
Copyright
Copyright © Applied Probability Trust 1972 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Ali Khan, M. S. (1970) Finite dams with inputs forming a Markov chain. J. Appl. Prob. 7, 291–303.CrossRefGoogle Scholar
[2] Ali Khan, M. S. and Gani, J. (1968) Infinite dams with inputs forming a Markov chain. J. Appl. Prob. 5, 72–83.CrossRefGoogle Scholar
[3] Boas, R. P. Jr. and Kac, M. (1945) Inequalities for Fourier transforms of positive functions. Duke Math. J. 12, 189–206.Google Scholar
[4] Foster, F. G. (1953) On the stochastic matrices associated with certain queueing problems. Ann. Math. Statist. 24, 355–360.CrossRefGoogle Scholar
[5] Gani, J. (1969) Recent advances in storage and flooding theory. Adv. Appl. Prob. 1, 90–110.CrossRefGoogle Scholar
[6] Lloyd, E. H. (1963) Reserviors with serially correlated inflows. Technometrics 5, 85–93.Google Scholar
[7] Lloyd, E. H. (1963) A probability theory of reservoirs with serially correlated inputs. J. Hydrol. 1, 99–128.CrossRefGoogle Scholar
[8] Lloyd, E. H. (1967) Stochastic reservoir theory. Adv. Hydroscience 4. Academic Press Inc., New York.Google Scholar
[9] Odoom, S. and Lloyd, E. H. (1964) A note on the solution of dam equations. J. R. Statist. Soc. B 19, 181–206.Google Scholar
[10] 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
[11] Roes, P. B. M. (1971) The Finite Dam: A Study of the Timedependent, Stochastic Behaviour of Storage Systems with Additive Input. , Technological University, Delft.Google Scholar