Gaussian Diffusion Approximation of Closed Markov Models of Computer Networks

The authors consider a model of a computer network in which (because of the flow control mechanism that is selected) there are always $N$ messages. The model is described by a closed network of queues that form a multivariate birth and death process. Under conditions of heavy traffic, it is shown that as $N\to\infty$, the queue length vector, normed by the number $N$, converges uniformly in probability to the solution of a system of differential equations, while deviations of the queue lengths of order $\sqrt{N}$ from a deterministic limit converge weakly to a Gaussian diffusion process. The martingale methods of proof that are employed yield results under very natural constraints.