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Some results for dams with Markovian inputs

Published online by Cambridge University Press:  14 July 2016

R. M. Phatarfod  and
K. V. Mardia
R. M. Phatarfod*
Affiliation:
Monash University
K. V. Mardia
Affiliation:
University of Hull
*
∗ Research partly carried out when this author was holding a Science Research Council Senior Visiting Fellowship at the University of Hull, June-July 1970.
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Abstract

The paper considers the dam problem with Markovian inputs, with special reference to the serial correlation coefficient of the input process. An input model is proposed which by giving particular values to the parameters makes the stationary distribution of the inputs one of the standard discrete distributions. The probabilities of first emptiness before overflow are first obtained by using the Markovian analogue of Wald's Identity. From these, the stationary distributions of the dam content are obtained by a duality argument. Both, finite and infinite dams are considered.

Keywords

MARKOVIAN INPUT OF LINEAR REGRESSIVE KINDMARKOVIAN ANALOGUE OF WALD'SIDENTITYPROBABILITIES OF EMPTINESSSTATIONARY DISTRIBUTIONS OF DAM CONTENTDEPENDENCE ON SERIAL CORRELATION COEFFICIENT
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 166 - 180
Copyright
Copyright © Applied Probability Trust 1973 

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