Scheduling Networks of Queues: Heavy Traffic Analysis of a Multistation Closed Network

We consider the problem of finding an optimal dynamic priority sequencing policy to maximize the mean throughput rate in a multistation, multiclass closed queueing network with general service time distributions and a general routing structure. Under balanced heavy loading conditions, this scheduling problem can be approximated by a control problem involving Brownian motion. Although a unique, closed-form solution to the Brownian control problem is not derived, an analysis of the problem leads to an effective static sequencing policy, and to an approximate means of comparing the relative performance of arbitrary static policies. Several examples are provided that illustrate the effectiveness of our procedure.