Quasi-Reversible Networks and Product Form Distributions

This chapter addresses the following question for a Markov network process. Under what conditions is the stationary distribution of the process a product of stationary distributions associated with the nodes? We consider a network in which the state of each node may contain more information than the number of units at the node, and a network transition may be triggered by an internal node change as well as by a unit moving from one node to another. The network process is viewed as a linkage of certain artificial Markov “node processes” that mimic the operation of the nodes as if they were operating in isolation. The main results are necessary and sufficient conditions under which the stationary distribution of the network is a product of the stationary distributions of the individual node processes.