Marked point processes as limits of Markovian arrival streams
- 1 June 1993
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 30 (2) , 365-372
- https://doi.org/10.2307/3214845
Abstract
A Markovian arrival stream is a marked point process generated by the state transitions of a given Markovian environmental process and Poisson arrival rates depending on the environment. It is shown that to a given marked point process there is a sequence of such Markovian arrival streams with the property that as m →∞. Various related corollaries (involving stationarity, convergence of moments and ergodicity) and counterexamples are discussed as well.Keywords
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