A method for calculating the marginal probabilities of states of cyclic queueing systems (Q1289163)

The paper considers a queueing system without losses consisting of one server and \(N\) independent Poisson input flows. Demands from the \(i\)th flow form the \(i\)th queue. Queues are served in cyclic order \(1\to 2\to 3\to\cdots\to N\to 1\). Server needs some time to switch over queues and processes all demands found in queue at the beginning of servicing. Let \(n_k\) be the length of the \(k\)th queue. The paper suggests a numerical method for calculating the stationary distribution of \((n_1,n_2,\dots, n_N)\).