Multiplicativity of a Stationary Distribution of an Open Queueing Network with Standard Nodes and Single-Type Calls

We consider open queueing networks with Markov routing, standard nodes, and one type of completely random arrivals. We assume that nodes with Poisson flow of arrivals, being isolated from the network, are described by continuous-time Markov chains. Under certain conditions, we establish necessary, sufficient, and necessary-and-sufficient conditions for the stationary distribution of the process describing the network to be representable as a product of factors characterizing the separate nodes.