Heavy traffic analysis of maximum pressure policies for stochastic processing networks with multiple bottlenecks

A class of open processing networks operating under a maximum pressure policy is considered in the heavy traffic regime. We prove that the diffusion-scaled workload process for a network with several bottleneck resources converges to a semimartingale reflecting Brownian motion (SRBM) living in a polyhedral cone. We also establish a state space collapse result that the queue length process can be lifted from the lower-dimensional workload process.