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A storage process by semi-Markov input

Published online by Cambridge University Press:  01 July 2016

Lajos Takács
Lajos Takács*
Affiliation:
Case Western Reserve University, Cleveland, Ohio
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Abstract

A sequence of random variables η 0, η 1, …, ηn , … is defined by the recurrence formula ηn = max (η n–1 + ξn , 0) where η 0 is a discrete random variable taking on non-negative integers only and ξ 1, ξ 2, … ξn , … is a semi-Markov sequence of discrete random variables taking on integers only. Define Δ as the smallest n = 1, 2, … for which ηn = 0. The random variable ηn can be interpreted as the content of a dam at time t = n(n = 0, 1, 2, …) and Δ as the time of first emptiness. This paper deals with the determination of the distributions of ηn and Δ by using the method of matrix factorisation.

Keywords

SEMI-MARKOV PROCESSESMATRIX FACTORISATIONSTORAGE PROCESSESDISTRIBUTION OF THE CONTENTDISTRIBUTION OF THE TIME OF FIRST EMPTINESS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 4 , December 1975 , pp. 830 - 844
Copyright
Copyright © Applied Probability Trust 1975 

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