Using singular perturbated systems of differencial equations of infinite order for countable Markov chains analysis

Tikhonov-type Cauchy problems are investigated for systems of ordinary differential equations of infinite order with a small parameter μ and initial conditions. It is studying the singular perturbated systems of ordinary differential equations of infinite order of Tikhonov-type {equation presented} with the initial conditions x(t0,gx) = gx, y(t0,gy) = gy, where x,f ∈ X, X ∈ Rn are n-dimensional functions; y, F ∈ Y , Y l1are infinite-dimensional functions and {equation presented} and gy ∈ Y are given vectors, μ > 0 is a small real parameter. The results may be applied to the queueing networks, which arise from the modern telecommunications. Copyright © 2016 for the individual papers by the papers' authors.