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+ɛ moments on the interarrival times and processing times, we provide a conceptually simple proof of asymptotic optimality of the proposed policy.
"Heavy traffic analysis of open processing networks with complete resource pooling: Asymptotic optimality of discrete review policies." Ann. Appl. Probab. 15 (1A) 331 - 391, February 2005. https://doi.org/10.1214/105051604000000495