A network of priority queues in heavy traffic: One bottleneck station.

In this paper we consider an open queueing network having multiple classes, priorities, and general service time distributions. In the case where there is a single bottleneck station we conjecture that normalized queue length and sojourn time process converge, in the heavy traffic limit, to one dimensional reflected Brownian motion, and present expressions for its drift and variance. The conjecture is motivated by known heavy traffic limit theorems for some special cases of the general model, and some conjectured "Heavy Traffic Principles' derived from them.