LAUSR

A system with heterogeneous servers, Poisson stream with Markov modulation, and instant feedback is studied. Primary requests are serviced in a high-speed server, and after servicing, each request, according to the Bernoulli scheme, either leaves the system or requires re-servicing. Repeated requests are serviced in a slow server; at the same time, after servicing, these requests also either leave the system or require repeated servicing in a slow server, according to the Bernoulli scheme. If at the moment of the arrival of the primary request the length of the queue of such requests exceeds a certain threshold value and the slow server is free, then the incoming request, according to the Bernoulli scheme, is either sent to the slow server or joins it when its turn to do so. It is considered that the lengths of the queues in front of each server are infinite. An adequate mathematical model of the system under study is constructed in the form of a three-dimensional Markov chain with an infinite state space. The ergodicity condition for this circuit is obtained, an approximate algorithm for calculating the stationary probabilities of the states is proposed, and its high level of accuracy is shown. The results of the numerical experiments are presented.