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Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains. (English) Zbl 0806.60052
A two-dimensional continuous time process is considered. The first component is a Markov chain and the second component is a continuous nonnegative function whose derivative depends on the first component. This implies that the second component can be given in term of a fluctuating additive functional. To investigate stationary distribution of this process a theorem about Wiener-Hopf factorization of Markov chains is proved. Some applications to fluid flow models with infinite and finite buffer are considered.
Reviewer: G.Falin (Moskva)

MSC:
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60K25 Queueing theory (aspects of probability theory)
60K15 Markov renewal processes, semi-Markov processes
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