BACKGROUND
Queueing networks are of current relevance for modelling computer systems, communication networks and complex manufacturing systems. Many of these systems have stations that can process more than one class of customer or job (so-called multiclass networks) and have complex feedback structures. Generally these systems cannot be analyzed in closed form and frequently are heavily loaded. One method for analyzing the performance of such systems is to approximate them by more tractable objects.

A certain class of diffusion processes, known as reflecting Brownian motions in polyhedral domains, have been shown to approximate the queue length processes in single class queueing networks and some multiclass queueing networks under conditions of heavy traffic (i.e., when the networks are heavily loaded). There is now a substantial theory for these diffusion processes, although some open problems remain. One of the outstanding challenges in current research on approximate models for queueing networks is to understand which multiclass networks can be approximated by reflecting Brownian motions in heavy traffic and to prove limit theorems justifying such approximations. In the last few years there have been some surprises both with regard to the stability of multiclass queueing networks and to their behavior in heavy traffic.

OUTLINE
The lectures will be concerned with approximation of queueing networks in heavy traffic and study of the related diffusion processes.