Multiplicativity of Markov chains with multiaddress routing (Q1812361)

A multiplicativity criterion known for a single class queueing network is extended to the network with multiaddress routing in which case a departing call may arrive at several stations simultaneously. A criterion of multiplicativity of the limit distribution of a Markov network process is found. This criterion includes a set of balance equations (in particular, partial balance) between network process distribution and those of isolated nodes. This criterion is also applied to the network with quasi-reversible and arrival ineffective stations.