We are studying the quasi-birth-death process and the property of weak ergodicity. Using the C-matrix method, we derive estimates for the rate of convergence to the limiting regime for the general case of the PH/M/1 model, as well as the particular case when m=3. We provide a numerical example for the case m=3, and construct graphs showing the probability of an empty queue and the probability of p1(t).
We consider the time-inhomogeneous Prendiville model with failures and repairs. The property of weak ergodicity is considered, and estimates of the rate of convergence for the main probabilistic characteristics of the model are obtained. Several examples are considered showing how such estimates are obtained and how the limiting characteristics themselves are constructed.
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