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A rate-conservative principle for stationary piecewise Markov processes

Published online by Cambridge University Press:  01 July 2016

Tomasz Rolski
Tomasz Rolski*
Affiliation:
Wrocław University
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Abstract

A stationary process yt, t ∈ R1 is considered which is Markov between points of changeover from a stationary point process, and at these points it changes over according to a distribution dependent only on the value of yt just before the change is analysed. An explicit form of a rate-conservative principle is stated, and its relationship with formulae relating the distribution of the process at an instant t and the distribution at a point of changeover is shown. The theory is applied to discrete state processes and to processes which are generalizations of the Takács processes, and is also applied in the theory of G/M/l and G/G/k queues to obtain relations between distributions of a process and some process imbedded in it.

Keywords

PIECEWISE MARKOV PROCESSRATE CONSERVATIVE PRINCIPLEIMBEDDED PROCESSG + M/G/1 QUEUEG/M/1 QUEUEG/G/k QUEUE
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 2 , June 1978 , pp. 392 - 410
Copyright
Copyright © Applied Probability Trust 1978 

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