Analysis of nonlinear delay differential equation models of TCP/AQM protocols using sums of squares

The simplest adequate models for congestion control for the Internet are in the form of deterministic nonlinear delay differential equations. However the absence of efficient, algorithmic methodologies to analyze them at this modelling level usually results in the investigation of their linearizations including delays; or in the analysis of nonlinear yet undelayed models. In this paper we present an algorithmic methodology for efficient stability analysis of network congestion control schemes at the nonlinear delay-differential equation model level, using the Sum of Squares decomposition and SOSTOOLS.