A Heavy Traffic Limit Theorem for Networks of Queues with Multiple Customer Types

The central result of this paper is a heavy traffic limit theorem for the vector of total station workloads in an open network of queues with multiple customer types, under first-come-first-served and priority disciplines. The limit process is a regulated Brownian motion on the nonnegative orthant, with parameters specified from the first two moments of the interarrival and service time distributions and a matrix of reduced routing information. Through the phenomenon of state space collapse, associated limit results for queue length, workload and sojourn time processes by customer type are obtained jointly as simple transformations of the total workload limit process. Diffusion approximations based on the theorem are discussed.