A rate-conservative principle for stationary piecewise Markov processes
- 1 June 1978
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 10 (2) , 392-410
- https://doi.org/10.2307/1426942
Abstract
A stationary processyt,t∈R1is 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 ofytjust 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 instanttand 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 ofG/M/landG/G/kqueues to obtain relations between distributions of a process and some process imbedded in it.Keywords
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