Bifurcation analysis for the Internet congestions

Abstract

The bifurcation and chaotic behavior of TCP may cause heavy oscillation of average queue length at routers and induce network instability. In this context, congestion control in the Internet is a challenging problem of key importance. This work presents a new discrete dynamical model of Random Early Detection (RED) using beta distribution for controlling bifurcations and chaos in the internet congestion control. The numerical analysis and the simulation experiments show that this new Active Queue Management (AQM) model can obtain the stable average queue length to the desired fix point. The model programmed with Python and Mathematica incorporates new parameters (α, β) that make it possible to stabilize oscillations of averaged router queue length and to be close to stationary state.