Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T21:44:45.200Z Has data issue: false hasContentIssue false
  • English
  • Français

On the time to first overflow in dams with inputs forming a Markov chain

Published online by Cambridge University Press:  14 July 2016

Douglas P. Kennedy
Douglas P. Kennedy*
Affiliation:
University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

A finite dam is studied in which the net input in each period, i.e. the excess of input over demand, is a function of a Markov chain. By using a martingale, the joint distribution of the time to first overflow and the cumulative unsatisfied demand until overflow is investigated. The probability of overflow before the unsatisfied demand exceeds a fixed level is also considered.

Keywords

FINITE DAMMARKOV INPUTSFIRST OVERFLOWFIRST-PASSAGE TIMEMARTINGALES
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 1 , March 1978 , pp. 171 - 178
Copyright
Copyright © Applied Probability Trust 1978 

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] Collings, P. S. (1974) Dams with random outputs. J. Appl. Prob. 11, 858–861.Google Scholar
[2] Kennedy, D. P. (1976) Some martingales related to cumulative-sum tests and single-server queues. Stoch. Proc. Appl. 4, 261–269.CrossRefGoogle Scholar
[3] Pakes, A. G. (1973) On dams with Markovian inputs. J. Appl. Prob. 10, 317–329.CrossRefGoogle Scholar
[4] Seneta, E. (1973) Non-Negative Matrices. Allen and Unwin, London.Google Scholar