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

Abstract

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.