Traffic flows and product form solutions in stochastic transfer networks

This paper focuses on product form and related tractable stationary distributions in a general class of stochastic networks with finite numbers of nodes such that their network states are changed through signal transfers as well as internal transitions. Signals may be customers in traditional queueing applications, but we do not make any restriction on their effects at departing as well as arriving nodes. They may also instantaneously move around among different nodes. Furthermore, signal routing may depend on the whole network state. For analytical simplicity, we assume that the state space is countable. For such a network, we propose an abstract model, called a stochastic transfer network and consider the stationary distribution of the network state. We introduce conditional traffic rates for arrivals and departures. Using them, we consider when the network has product form or some other tractable stationary distributions.