A two dimensional fluid model for TCP/AQM analysis

TL;DR

This paper introduces a novel two-dimensional nonlinear fluid model for TCP/AQM systems, incorporating dual time bases to enhance accuracy and stability analysis, with practical traffic scenarios validating the approach.

Contribution

It develops a new 2D nonlinear fluid model considering queue and congestion window dynamics, and proposes a Lyapunov-based stability analysis with controller synthesis.

Findings

The model accurately captures TCP/AQM dynamics.

Stability conditions are derived using matrix inequalities.

Simulation scenarios confirm theoretical results.

Abstract

This work proposes a new mathematical model for the TCP/AQM system that aims to improve the accuracy of existing fluid models, especially with respect to the sequential events that occur in the network. The analysis is based on the consideration of two time bases, one at the queue's router level and the other at the congestion window level, which leads to the derivation of a new nonlinear two-dimensional fluid model for Internet congestion control. To avoid the difficult task of assessing stability of a 2D nonlinear dynamic model, we perform a local stability analysis of a 2D linear TCP AQM model. By constructing a new two dimensional second order Bessel Legendre Lyapunov functional, new matrix inequalities are derived to evaluate the stability of the 0-input system and to synthesize a feedback controller. Finally, two Internet traffic scenarios, with state space matrices for replicability, are presented, demonstrating the validity of the theoretical results.