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.

TCP AIMD dynamics over internet connections

“…These TCP dynamics are a result of the highly non-linear nature of its AIMD (Additive Increase and Multiplicative Decrease) congestion control mechanism reacting to stochastic dynamics of Internet traffic, more precisely the packet losses. Thus it is natural to expect TCP dynamics to be complicated, as indicated by preliminary studies [2], [21], [17], [16]. The first study on TCP dynamics using chaos theory is by Veres and Boda [21].…”

“…Using the ns-2 simulator, they have studied the congestion window dynamics of competing TCP streams. While these works demonstrate that transport dynamics can be chaotic, their scope is limited since they rely solely on simulation [21] or analysis [17], or use network configurations that are not typical of current Internet such as active queues [16]. To a large extent the exact nature of TCP dynamics over actual Internet connections is still an open question.…”

Controlling Bifurcation and Chaos in Internet Congestion Control Model

“…Recently, Ranjan and Abed showed that the TCP-RED could be approximately modeled as a first-order nonlinear map [Ranjan & Abed, 2002]. They found that the TCP-RED map exhibits a rich variety of irregular behaviors such as bifurcation and chaos.…”

Global stability of TCP/RED with many-flows: a numerical approach

“…Using the fixed point approach [16], we have C = 3 2f * = 6.70, where f * = 0.0389 is given by f * = 1 C(1+C/2) . From Figure 5, we can see that W (t) fluctuates around 6.71, which matches W (∞) = C = 6.70 using (5), and that the normalized queue size converges to 4.94, which is also approximately equal to Q(∞) given by (6). We see that as the number of flows increases, the fluctuation of the "averaged" values becomes smaller, and this suggests that our normalized model can effectively capture the system behavior, when the number of flows is large.…”

“…Stability is one of the important issues of TCP/AQM (Active Queue Management) [1], [2], [3], [4], [5], [6], [7]. According to [1], an unstable TCP/AQM system may increase delay and jitter, which can be detrimental to some delay-jitter sensitive applications, and cause link under-utilization.…”