Heavy traffic analysis of open processing networks with complete resource pooling: asymptotic optimality of discrete review policies

Abstract

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.Comment: Published at http://dx.doi.org/10.1214/105051604000000495 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org