Nonlinear instabilities in TCPRED

Abstract — This work develops a discrete time feedback system model for a simplified TCP (Transmission Control Protocol) network with RED (Random Early Detection [2]) control. The model involves sampling the buffer occupancy variable at certain instants. The dynamical model is used to analyze the TCP-RED operating point and its stability with respect to various RED controller and system parameters. Bifurcations are shown to occur as various system parameters are varied. These bifurcations, which involve emergence of oscillatory and/or chaotic behavior, may provide an explanation for the parameter sensitivity observed in practice. The bifur-cations arise due to the presence of a nonlinearity in the characteristics of TCP throughput as a function of drop probability at the gateway. Among the bifurcations observed in the system are the period-doubling bifurcation and border collision bifurcations. The bifurcations are studied analytically, numerically, and experimentally. I