Diffusion approximation of state dependent G-networks under heavy traffic

This paper is concerned with the characterization of weak-sense limits of state-dependent G-network under heavy traffic. It is shown that, for a certain class of networks (which includes a two layer feedforward network and two queues in tandem), it is possible to approximate the number of customers in the queue by a reflected stochastic differential equation. The benefits of such an approach are that it describes the transient evolution of these queues and allows the introduction of controls, inter alia. We illustrate the application of the results with numerical experiments.