Asymptotic diffusion analysis of $MMP P |M|N$ queuing systems with feedback

We present the results of the study of an $ N $-linear queuing system with feedback. The input flow is a Markov modulated Poisson process (MMPP). We use asymptotic diffusion analysis to find the probability distribution of the number of requests in the orbit and the number of busy servers in the system. Simulation results, as well as a numerical comparison of our method with asymptotic analysis method, are presented.