Large Deviations for the Stationary Measure of Networks Under Proportional Fair Allocations

• 成果类型: Article
• 署名作者: Jonckheere, Matthieu; Lopez, Sergio
• 署名单位: Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); University of Buenos Aires; Universidad Nacional Autonoma de Mexico
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2013.0605
• 发表日期: 2014
• 页码: 418-431
• 关键词: insensitivity

摘要

We address a conjecture introduced by Massoulie [Massoulie L (2007) Structural properties of proportional fairness: Stability and insensitivity. Ann. Appl. Probab. 17(3):809-839], concerning the large deviations of the stationary measure of bandwidth-sharing networks functioning under the proportional fair allocation. For Markovian networks, we prove that proportional fair and an associated reversible allocation are geometrically ergodic and have the same large deviations characteristics using Lyapunov functions and martingale arguments. For monotone networks, we give a more direct proof of the same result, relying on stochastic comparisons, that holds for general service time distribution. These results support the intuition that proportional fairness is close to allocations of service being insensitive to the service time distribution.