Closed Queueing Network with a Multiline Transmission Channel

A closed queueing network with $n$ demands is considered. The demands are transmitted from one node of the network to another over an $r$-line transmission channel, $1\leq r\leq n$. The transmission time of the demands in the channel and the service time at the network nodes are assumed to be exponentially distributed random variables. The stationary probability distribution of the network states is found, which has a rather simple analytical form.