Brownian Networks with Discretionary Routing

Motivated by scheduling problems that arise in flexible manufacturing systems, we develop a heuristic procedure to obtain effective flow control (sequencing, routing, and input control) policies for multiclass queueing networks. The procedure employs a Brownian model of J. M. Harrison that approximates a multiclass queueing network with dynamic scheduling capability, if the total load imposed on each station in the queueing network is approximately equal to that station's capacity. In this paper, each customer class may be served at any of several different stations, and thus dynamic routing decisions are added to the sequencing and input control decisions already present in Harrison's model. Using previous heavy traffic results as a guide, we observe that, under heavy traffic conditions, a queueing network routing its customers to the queue where they will incur the shortest expected delay behaves very much like the reduced queueing network formed by pooling the appropriate servers. This observation leads to a proposed reduction of a Brownian network with discretionary routing to a simpler Brownian network without discretinary routing. Computational results indicate that combining this reduction with previous analysis of Brownian networks without discretionary routing leads to effective flow control policies for many moderately sized queueing network scheduling problems.