Asymptotic analysis of the closed queueing structure with time-dependent service parameters

Abstract

A closed queueing structure is considered in the paper; number of single-type messages is not constant and depends on time. The route of messages is given by arbitrary stochastic matrix of transition probabilities. An asymptotic analysis of this structure in case of large number of service requests con-ducted. The service parameters of each queueing system of this structure, as well as the probability of messages transition between systems, depend on time. A system of ordinary differential equations to calculate the average relative number of messages in each queueing system, depending on the time, was obtained.