An unified approach to signaling stochastic networks and their heavy traffic approximations

In this paper, we derive the heavy traffic approximation for a certain class of stochastic Petri nets (SPNs). Regarding this class, the novelty here is that we consider a state-dependent Poison-type network where the transitions are also state-dependent and they may have a finite set of possible outcomes, which have a similar effect to “routeing” in queueing systems. The model is general enough to include, for instance, G-networks with negative customers and triggers with no restriction on the topology, as a particular case. The main goal is to have a diffusion approximation which can be readily applied in several different practical problems that involve the transient evolution of quantities which suffer exchanges stochastically in time.