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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
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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

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 1 , March 1978 , pp. 171 - 178
Copyright
Copyright © Applied Probability Trust 1978 

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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