Nonlinear Instabilities in TCP-RED

Abstract

Abstract-This work develops a discrete-time dynamical feedback system model for a simplified TCP network with RED control and provides a nonlinear analysis that can help in understanding observed parametric sensitivities. The model describes network dynamics over large parameter variations. 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 system parameters are varied. These bifurcations, which involve the emergence of oscillatory and/or chaotic behavior, shed light on the parametric sensitivity observed in practice. The bifurcations arise due to the presence of a nonlinearity in the TCP throughput characteristic as a function of drop probability at the gateway. Among the bifurcations observed in the system are period doubling and border collision bifurcations. The bifurcations are studied analytically, numerically, and experimentally.

A non-equilibrium analysis and control framework for active queue management

“…In addition, stability and robustness properties of the resulting system with respect to time delays have been identified. A nonlinear and bifurcation analysis of RED on a TCP network has been conducted in [22] where a discrete-time dynamical model is used to analyze the TCP-RED operating point and its stability with respect to various RED controller and system parameters. In a subsequent study [23], a stochastic model of a bottleneck RED gateway under a large number of heterogeneous TCP flows has been proposed and the asymptotic behavior of the system has been investigated.…”

“…Although much of control-oriented analysis and design has appeared within linear settings, there is significant evidence in literature for complex and chaotic queue behavior in Internettype networks and their models [3], [22], [25], [26]. Nonequilibrium fluctuations in queue behavior has been observed both experimentally and numerically [25], [27].…”

“…Nonequilibrium fluctuations in queue behavior has been observed both experimentally and numerically [25], [27]. For appropriate parameter values, the simplified fluid models also exhibit persistent non-equilibrium behavior [3], [22], [28]. The nonequilibrium behavior in queues may be due to random noise or could arise as self-excited "chaotic oscillations" and there are suggestions for both in the literature [27].…”

“…Papers concerned with deriving mean or limit models [23], [29], [30], obtaining AQM performance with linear control methods [11], [31], or with carrying out describing function based analysis [32] typically assume a random noise. The papers concerned with local instability/bifurcation analysis [22], [33]- [36], and (global) numerical investigations [1], [3], [22] using deterministic fluid models show these oscillations as self-excited. With simple fluid models, analytical methods from bifurcation theory have been used to show that these self-excited oscillations can arise as a result of supercritical Hopf bifurcation [33], [35], [37] and of period doubling and border-collision bifurcations [22].…”

“…The papers concerned with local instability/bifurcation analysis [22], [33]- [36], and (global) numerical investigations [1], [3], [22] using deterministic fluid models show these oscillations as self-excited. With simple fluid models, analytical methods from bifurcation theory have been used to show that these self-excited oscillations can arise as a result of supercritical Hopf bifurcation [33], [35], [37] and of period doubling and border-collision bifurcations [22].…”