Heavy Traffic Analysis of Open Processing Networks with Complete Resource Pooling: Asymptotic Optimality of Discrete Review Policies

We consider a class of open stochastic processing networks, with feedback routing and overlapping server capabilities, in heavy traffic. The networks we consider satisfy the so-called complete resource pooling condition and therefore have one dimensional approximating Brownian control problems. We propose a simple discrete review policy for controlling such networks. Assuming 2 + epsilon moments on the interarrival times and processing times, we provide a conceptually simple proof of asymptotic optimality of the proposed policy.