Control-Theoretic Methods for the Analysis and Design of High-Speed Networks Carolyn Beck and R. Srikant Over the last few years, a significant amount of research activity in networking has been devoted to the study of congestion control in the Internet. New algorithms have been suggested for congestion controllers at the sources and active queue management at the routers. While the success of the mathematical modelling approach to congestion control has been quite remarkable, many important problems remain open. In this proposal, we have targeted a few of these problems which have a control-theoretic flavor and therefore, we believe, would benefit from analysis using linear or nonlinear system-theoretic methods. The practical impact of the proposed research would be the development of algorithms which will result in a loss-free, delay-free Internet, thus enabling the users of the Internet to enjoy levels of quality of ser-vice that are not seen today. Further, our work will lay the groundwork for future Internet algorithms when the access speeds are expected to grow by several orders of magnitude as compared to today's networks. Scalable algorithms for high-speed networks are already under development; however, these schemes pri-marily address the fact that today's TCP is not scalably stable. On the other hand, our work will not only address scalable stability, it also aims to improve the quality of service seen by Internet users by essentially eliminating queueing delays and large buffer build-ups which lead to packet losses. Intellectual Merit Our recent work has established scalable local stability of a class of congestion man-agement algorithms for the Internet with a fixed number of sources, and robustness of these algorithms in the special case of a link accessed by many sources. While we have only scratched the surface of this rich class of problems, the appealing features, such as distributed implementation, robustness, full network utilization, etc., observed in the preliminary work indeed ask for a more comprehensive study of the underlying issues in a broader context. Specifically, we would like to know whether we can establish the global stability of these algorithms for general topology networks, quantify their robustness to worst-case disturbance as well as stochastic disturbances, and study their stability properties when there are source arrivals and departures. In the process, we plan to appeal to the rich literature on model reduction for large-scale control systems. Broad Impact One of the PIs teaches a graduate course on Modeling and Control of High-Speed Networks (ECE 459). The results from this project will be incorporated into that course. We have prior experience with employing undergraduates to work on research projects in the area of network design and control. If this project is funded, we will continue to do the same. The algorithms developed as a result of this project will be implemented in Internet lab, housed in the Coordinated Science lab and directed by one of the PIs. Over the past four years, we have advised six graduate students and two post-doctoral research associates from under-represented groups in engineering. We will continue our efforts to recruit students from under-represented groups for graduate studies. One of the PIs teaches undergraduate courses in the Department of General Engineering. Traditionally, this department has a high percentage of women in the undergraduate population compared to other engineering departments. By incorporating some of the results of this project in the undergraduate courses in General Engineering, we hope to stimulate interest in this area among students from this group. P-1
