Title of article :
ON A DISTRIBUTION OF THE PROCESS DESCRIBING A SERVICE SYSTEM WITH UNRELIABLE DEVICES
Author/Authors :
ALIEV, T.M Institute of Control Systems - Azerbaijan National Academy of Sciences - Baku, Azerbaijan , IBAYEV, E.A Institute of Control Systems - Azerbaijan National Academy of Sciences - Baku, Azerbaijan , MAMEDOV, V.M Institute of Control Systems - Azerbaijan National Academy of Sciences - Baku, Azerbaijan
Abstract :
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.
Keywords :
Poisson process , Laplace transformation , Generating function , Markov chain , Homogeneous with respect to the second component
Journal title :
Turkish World Mathematical Society Journal of Applied and Engineering Mathematics
