Optimal control problems for heavy traffic queues

The author is concerned with optimal or nearly optimal routing of a queueing system under heavy traffic conditions. Optimal and nearly optimal control problems for a queueing network is examined. Various inputs and service interruptions are the controls. It is shown that the scaled controlled reflected system converges to a controlled limit reflected diffusion and the optimal policies for the limit when adapted to the physical system are nearly optimal. The martingale problem methods are utilized in the analysis.