Although the internet's origins lie in computer and communication technology, control and stability theory have also had a major influence on its development. After the development of the additive increase, multiplicative decrease algorithm by Jacobson in 1988, the first significant Active Queue Management (AQM) algorithm introduced was Random Early Detection (RED). In RED, the basic idea is to let the senders know about a high queue occupancy situation by increasing the drop probability at the gateways as a linear function of the time-averaged queue occupancy. Field observations of anomalous behavior for TCP networks with and without deployment of RED have been made that show irregular load batching, load oscillations, and high parametric sensitivity. Given the heterogeneity of the internet, and the associated wide variations of parameters, extending the range of stable operation in parameter space is clearly very important. In this research program, tools from nonlinear dynamical systems and from bifurcation and chaos control will be harnessed for the analysis and control of congestion in networks with one or several bottlenecks with TCP-type and/or UDP-type (User Datagram Protocol) traffic. The project emphasizes work of a fundamental nature to develop an understanding of network congestion dynamics and address some of the difficult systems issues that are at the heart of the congestion avoidance and control problem. The project builds on recent work of the PI's group on the analysis of nonlinear dynamics in TCP-RED and mixed traffic networks. The project also leverages past contributions of the PI on control of nonlinear instabilities (bifurcation control) and on closed-loop monitoring of the stability of nonlinear uncertain systems.
