ASYMPTOTIC OPTIMALITY OF MAXIMUM PRESSURE POLICIES IN STOCIIASTIC PROCESSING NETWORKS

• 成果类型: Article
• 署名作者: Dai, J. G.; Lin, Wuqin
• 署名单位: University System of Georgia; Georgia Institute of Technology; Northwestern University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP522
• 发表日期: 2008
• 页码: 2239-2299
• 关键词: multiclass queuing-networks; state-space collapse; heavy traffic analysis; DIFFUSION APPROXIMATIONS; brownian networks; parallel servers; threshold policy; SYSTEM; workload; switch

摘要

We consider a class of stochastic processing networks. Assume that the networks satisfy a complete resource pooling condition. We prove that each maximum pressure policy asymptotically minimizes the workload process in a stochastic processing network in heavy traffic. We also show that, under each quadratic holding cost structure, there is a maximum pressure policy that asymptotically minimizes the holding cost. A key to the optimality proofs is to prove a state space collapse result and a heavy traffic limit theorem for the network processes under a maximum pressure policy. We extend a framework of Bramson [Queueing Systems Theory Appl. 30 (1998) 89-148] and Williams [Queueing Systems Theory Appl. 30 (1998b) 5-25] from the multi-class queueing network setting to the stochastic processing network setting to prove the state space collapse result and the heavy traffic limit theorem. The extension can be adapted to other studies of stochastic processing networks.