A Stochastic Network Under Proportional Fair Resource Control-Diffusion Limit with Multiple Bottlenecks

• 成果类型: Article
• 署名作者: Ye, Heng-Qing; Yao, David D.
• 署名单位: Hong Kong Polytechnic University; Columbia University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1120.1047
• 发表日期: 2012
• 页码: 716-738
• 关键词: state-space collapse; reflecting brownian motions; bandwidth-sharing policy; heavy-traffic optimality; Asymptotic Optimality; invariance-principle; STABILITY; fluid; MODEL; workload

摘要

We study a multiclass stochastic processing network operating under the so-called proportional fair allocation scheme, and following the head-of-the-line processor-sharing discipline. Specifically, each server's capacity is shared among the job classes that require its service, and it is allocated, in every state of the network, among the first waiting job of each class to maximize a log-utility function. We establish the limiting regime of the network under diffusion scaling, allowing multiple bottlenecks in the network, and relaxing some of the conditions required in prior studies. We also identify the class of allocation schemes among which the proportional fair allocation minimizes a quadratic cost objective function of the diffusion-scaled queue lengths, and we illustrate the limitation of this asymptotic optimality through a counterexample.