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On the rate of beta-mixing and convergence to a stationary distribution in continuous-time Erlang-type systems. (English. Russian original) Zbl 1235.60098

Probl. Inf. Transm. 46, No. 4, 382-389 (2010); translation from Probl. Peredachi Inf. 46, No. 4, 122-129 (2010).
Summary: We establish sufficient conditions ensuring a polynomial rate of convergence to a stationary distribution and of beta-mixing for continuous-time Erlang-type systems. Our results are a natural complement both to results of Erlang himself, dating back to the beginning of the 20-th century, and to exponential estimates established later.

MSC:

60J27 Continuous-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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