PROPORTIONAL FAIRNESS AND ITS RELATIONSHIP WITH MULTI-CLASS QUEUEING NETWORKS
成果类型：
Article
署名作者：
Walton, N. S.
署名单位：
University of Cambridge
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/09-AAP612
发表日期：
2009
页码：
2301-2333
关键词：
摘要：
We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level model found is insensitive. A large deviation principle for the stationary distribution of these multi-class queueing networks is also found. Its rate function has a dual form that coincides with proportional fairness. We then give the first rigorous proof that the stationary throughput of a multi-class single-server queueing network converges to a proportionally fair allocation. This work combines classical queueing networks with more recent work on stochastic flow level models and proportional fairness. One could view these seemingly different models as the same system described at different levels of granularity: a microscopic, queueing level description; a macroscopic, flow level description and a teleological, optimization description.