On controlled poisson processes

We consider a special class of two-dimensional Markov processes, finding the relationship between transition probabilities of two such classes.Publisher's Versio

On a distribution of the process describing a service system with unreliable devices

In the paper, the distribution is found for the process {ηt, ξt}, t ≥ 0, in the terms of Laplace transformation. The considered process describes the queuing system with nonhomogeneous Poisson stream of demands and n unreliable devices. It is essential that the process {ηt, ξt}, t ≥ 0, for ξt ≥ n is a homogeneous with respect to the second component Markov process. The results obtained in the paper are based on the theory of matrices and solution of the system of linear integral equations.Publisher's Versio