Stability analysis of the Internet congestion control

Abstract

The Internet has become an important medium of information transfer nowadays. The TCP/IP protocol suite and the interconnected gateways provide reliable channels for the flow of information which are evenly shared among different connections. It has been known that a bottleneck RED (Random Early Detection) gateway can become oscillatory when regulating multiple identical TCP (Transmission Control Protocol) flows. In this thesis, we will study the stability issue in the TCP-RED system. The stability boundary of the TCP-RED system depends on many network parameters, making the adjustment of the RED gateway a difficult task. Based on a fluid-flow model (FFM), we formulate analytical conditions that describe the stability boundary of the RED gateway which depends on the number of TCP Reno connections. The proposed model accurately generates a stability boundary surface in a four dimensional space, which facilitates the adjustment of parameters for stable operation of the RED gateway. The accuracy of the analytical results has been verified using the ns-2 network simulator. We will use the fluid-flow model to derive the system characteristic frequency, and then compare it with the frequencies of the RED queue length waveforms observed from ns-2 simulations. The ns-2 simulator is the only viable simulation tool accepted by industry for verification purposes. Analysis of the TCP source frequency distribution reveals the occurrence of period doubling when the system enters the instability region as the filter resolution varies. Since random events and a large number of TCP flows are involved in the process of generating the average system dynamics, a statistical viewpoint is taken in the analysis. Our results reflect the true system behavior as they are based on data from ns-2 simulations rather than numerical simulations of analytical models. The physical mechanism of oscillation is explained in terms of the difference in the TCP source frequency and the TCP-RED system characteristic frequency. The detrended fluctuation analysis (DFA) method is used to analyze the stability of the Internet RED gateway. In DFA, time-series data are analyzed to generate a key parameter called power-law scaling exponent, which provides indication as to the long-range correlations of the time series. By examining the variation of the DFA scaling exponent when varying system parameters, we quantify the stability of the RED system in terms of system's characteristics. Finally, the random explicit congestion notification (ECN) marking distribution mechanism in RED gateways has been studied. The randomness of the RED ECN marking algorithm is implemented into the FFM. The new model is shown to have better dynamic performance, as verified by the waveforms provided by ns-2 simulations.