Optimal Routing in Closed Queueing Networks with State Dependent Queues

Optimal routing in closed queueing networks with state dependent queues is the focus of this paper. We seek a methodology and algorithm to efficiently solve the routing probabilities in closed systems. These systems may include multi-server exponential and general service finite capacity state dependent models as well as multi-chain systems. The state dependent models included within this paper extend the range of possible system applications with our algorithm to include transportation and material handling conveyor systems, pedestrian, and vehicular routing applications. Sometimes the networks will be purely state dependent M/G/c/c queues, while other times, there will be a mixture of M/M/c and M/G/c/c queues. These state dependent M/G/c/c queues are finite queues, while the workstations are infinite buffer queues. Because these networks have been shown to have a product form and the objective function in single chain networks is concave, we can achieve an optimal seeking algorithm. Numerous experiments are shown to illustrate the efficacy of the approach.