ИСТИНА

We investigate a generalized Jackson (open queueing) network with regenerative input flows. The system is unreliable, in a sense that every server is subject to a random environment generating breakdowns and repairs. We consider an infinite horizon and establish the theorem on the strong approximation of the vector of queue lengths by a reflected Brownian motion in an orthant. Bounds for the probability of deviations are given as well. As a corollary, we estimate the Wasserstein distance between the laws of queue lengths and of the reflected Brownian motion. Then, applying the local averaging techniques, we construct consistent estimates of limit process parameters and propose an approach to bottleneck recognition.