ON A DISTRIBUTION OF THE PROCESS DESCRIBING A SERVICE SYSTEM WITH UNRELIABLE DEVICES

In the paper, the distribution is found for the process {[[eta].sub.t],[[xi].sub.t]},t [greater than or equal to] 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 {[[eta].sub.t],[[xi].sub.t]},t [greater than or equal to] 0, for [[xi].sub.t] [greater than or equal to] 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. Keywords: Poisson process, Laplace transformation, Generating function, Markov chain, Homogeneous with respect to the second component. AMS Subject Classification: 60A10, 60J25, 60G10.