A STOCHASTIC ANALYSIS OF RESOURCE SHARING WITH LOGARITHMIC WEIGHTS

• 成果类型: Article
• 署名作者: Robert, Philippe y; Veber, Amandine
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1057
• 发表日期: 2015
• 页码: 2626-2670
• 关键词: fluid limit; STABILITY

摘要

The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has x requests to transmit, then it receives a fraction of the capacity proportional to log(1 + x), the logarithm of its current load. A detailed fluid scaling analysis of such a network with two nodes is presented. It is shown that the interaction of several time scales plays an important role in the evolution of such a system, in particular its coordinates may live on very different time and space scales. As a consequence, the associated stochastic processes turn out to have unusual scaling behaviors. A heavy traffic limit theorem for the invariant distribution is also proved. Finally, we present a generalization to the resource sharing algorithm for which the log function is replaced by an increasing function. Possible generalizations of these results with J > 2 nodes or with the function log replaced by another slowly increasing function are discussed.