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Level crossings and stationary distributions for general dams

Published online by Cambridge University Press:  14 July 2016

Michael Rubinovitch  and
J. W. Cohen
Michael Rubinovitch*
Affiliation:
Technion — Israel Institute of Technology
J. W. Cohen*
Affiliation:
University of Utrecht
*
∗Postal address: Faculty of Industrial and Management Engineering, Technion–Israel Institute of Technology, Haifa, Israel. Research supported by Air Force Office of Scientific Research Grant No. 74–2733 while the author was on leave at Northwestern University.
∗∗Postal address: State University of Utrecht, Mathematical Institute, Budapestlaan 6, Utrecht 2506, The Netherlands.
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Abstract

Level crossings in a stationary dam process with additive input and arbitrary release are considered and an explicit expression for the expected number of downcrossings (and also overcrossings) of a fixed level, per time unit, is obtained. This leads to a short derivation of a basic relation which the stationary distribution of a general dam must satisfy.

Keywords

LEVEL CROSSINGSADDITIVE INPUTDAMSSTATIONARY DISTRIBUTIONUPCROSSINGSDOWNCROSSINGSREGENERATIVE PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 218 - 226
Copyright
Copyright © Applied Probability Trust 1980 

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References

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