Symmetrical token ring lan with messages of different types and gated service

We study a symmetrical ring topology local network with a token access protocol with number $N$ of stations, each of them has $n$ buffers of capacity $1$ for each type of incoming messages. After the token arrives at any station, all the messages in the buffers are serviced in accordance with the gated service discipline. Incoming messages of n types are Poisson, independent intensity flows $\lambda_i$, $1\leqslant i\leqslant n$ n for an arbitrary station. A system of vector-matrix equations is presented, which makes it possible to calculate the probabilities of stationary states, as well as the main characteristics of the studied ring network.