Bounds on the Rate of Convergence for a Nonstationary Two – Class Priority Queuing System

In this article, an approach to studying two-dimensional processes of birth and death was considered using the example of a non-stationary two – class priority queuing system. An estimate of the rate of convergence of the original process was obtained, with the help of which one can study, first of all, the projections of process Z(t). Estimates for the projection of process Z(t) = (X(t),Y (t)) were obtained using the logarithmic norm method. A numerical example illustrates the behavior of projections X(t) and Y (t) of the original two-dimensional process Z(t); graphs are constructed for the probability of an empty queue, the average number of customers in the system for specific intensity functions λ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>(t),μ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>(t),λ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>(t),μ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>(t). An estimate of the rate of convergence of the original process Z(t) and an estimate of the limiting average were also obtained.