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Geometric decay of the steady-state probabilities in a quasi-birth-and-death process with a countable number of phases. (English) Zbl 0985.60074
The authors study the properties of the stationary distribution of a quasi-birth-and-death process with a countable number of phases in each level with discrete and continuous time. The results are applied to a parallel queueing system. As an appendix the modified parallel queueing model is considered.

MSC:
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60K25 Queueing theory (aspects of probability theory)
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