Characterization of network stationary distribution with batch moving in geometric product form (Q2888241)

A network with non-standard batch arrivals and transfers is considered. It is supposed that two Poisson flows of customer batches (general and additional) enter the empty nodes. The service time is modeled by the exponential distribution. The traffic of batches is described by an irreducible Markov matrix. Necessary and sufficient conditions are established for the existence of the stationary distribution of the batches in the system where that distribution can be expressed by the product of geometric distributions.