Fluid-based analysis of a network of AQM routers supporting TCP flows with an application to RED

TLDR: This paper uses jump process driven Stochastic Differential Equations to model the interactions of a set of TCP flows and Active Queue Management routers in a network setting and presents a critical analysis of the RED algorithm.

Abstract: In this paper we use jump process driven Stochastic Differential Equations to model the interactions of a set of TCP flows and Active Queue Management routers in a network setting. We show how the SDEs can be transformed into a set of Ordinary Differential Equations which can be easily solved numerically. Our solution methodology scales well to a large number of flows. As an application, we model and solve a system where RED is the AQM policy. Our results show excellent agreement with those of similar networks simulated using the well known ns simulator. Our model enables us to get an in-depth understanding of the RED algorithm. Using the tools developed in this paper, we present a critical analysis of the RED algorithm. We explain the role played by the RED configuration parameters on the behavior of the algorithm in a network. We point out a flaw in the RED averaging mechanism which we believe is a cause of tuning problems for RED. We believe this modeling/solution methodology has a great potential in analyzing and understanding various network congestion control algorithms.