互联网流量控制的朗之万模型及相变分析  

Langevin model of the flow control in the internet and its phase transition analysis

作　　者：樊华[1] 李理[1] 袁坚[1] 山秀明[1] 

机构地区：[1]清华大学电子工程系,北京100084

出　　处：《物理学报》2009年第11期7507-7513,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:60674048;60603068;60772053;60672142);国家重点基础研究发展计划(973)项目(批准号:2007CB307100-2007CB307105)资助的课题~~

摘　　要：为互联网中的流量控制协议构建恰当模型,从而阐明具体协议算法与网络宏观性能间的关系,一直是互联网研究者面临的重大挑战.本文通过逻辑演绎,建立了互联网传输控制协议下流量的朗之万方程.在此基础上,细致分析了主动队列管理算法的有效性,在理论上证明了此类算法存在从畅通态到拥塞态到瘫痪态的相变过程,并给出了相变临界点与系统参数的显式关系.本建模与分析方法虽以具体的主动队列管理算法为例,但其方法可以应用于一般的网络流量控制问题.One of the big challenges in the field of Internet research is to elucidate the relationship between micro-algorithms of the flow control protocols and macro-properties of the Internet with a proper model. In this paper, we build up a Langevin equation under the transmission control protocol using deductive method. Then we analyze the effectiveness of the active queue management based on the Langevin model. We have proved that there is a phase transition sequence from smooth state to congestion state then to paralysis state in all such kind of algorithms. We also provide explicit formulas of the critical points in terms of the system parameters. Although the model used in this paper focuses on a specific algorithm, we believe this method has a great potential in analyzing and understanding various network congestion control algorithms.

关 键 词：互联网 流量控制 朗之万方程 相变 

分 类 号：TP393.01[自动化与计算机技术—计算机应用技术]