Model Queue Management on Routers

Problems of modeling of active queue management (AQM) systems have been for a long time in the sphere of interests of authors. One of the areas of work was associated with a dynamic model of the control module Random Early Detection (RED) based on Poisson process driven stochastic differential equations. These equations are used in queuing theory quite recently, and not very well understood. As disadvantages of this approach the authors underlined its non-generic character. We describe the interaction between module RED and protocol TCP Reno. But its extension to other variants of the TCP protocol and the control module is not possible. Our group studied common approaches to modeling of such phenomena. As a result a method for randomization of one-step processes, allowing to obtain new models in a universal manner was developed. In this paper, the authors use this technique to model previously investigated RED module and protocol TCP Reno to demonstrate its applicability to this kind of problems. As a result an extended model of control module type RED for traffic type TCP Reno, was created. It contains previously studied model as a special case.

stochastic differential equations, master equation, Fokker- Planck equation, AQM, RED