Control-Theoretic Methods for the Analysis and Design of High-Speed Networks

高速网络分析与设计的控制理论方法在过去的几年里，大量的网络研究活动都致力于研究互联网中的拥塞控制。提出了新的拥塞控制器算法和路由器上的主动队列管理算法。虽然数学建模方法在拥塞控制方面取得了显著的成功，但仍有许多重要的问题有待解决。在本提案中，我们针对其中一些具有控制理论风味的问题，因此，我们相信，使用线性或非线性系统理论方法进行分析将受益。拟议研究的实际影响将是算法的发展，这些算法将导致无丢失、无延迟的互联网，从而使互联网用户能够享受到今天所未见的服务质量水平。此外，我们的工作将为未来的互联网算法奠定基础，届时接入速度预计将比今天的网络增长几个数量级。高速网络的可扩展算法已经在开发中；然而，这些方案主要解决了一个事实，即今天的TCP不具有可伸缩性稳定性。另一方面，我们的工作将不仅解决可扩展的稳定性，它还旨在通过消除排队延迟和导致数据包丢失的大量缓冲区建立来提高互联网用户所看到的服务质量。我们最近的工作已经建立了一类具有固定数量源的互联网拥塞管理算法的可扩展局部稳定性，以及这些算法在由许多源访问的链路的特殊情况下的鲁棒性。虽然我们只触及了这类丰富问题的表面，但吸引人的特性，如分布式实现、鲁棒性、充分的网络利用率等。，确实要求在更广泛的背景下对潜在问题进行更全面的研究。具体来说，我们想知道我们是否可以建立这些算法对一般拓扑网络的全局稳定性，量化它们对最坏情况干扰和随机干扰的鲁棒性，并研究它们在有源到达和离开时的稳定性。在此过程中，我们计划利用大量关于大型控制系统模型约简的文献。广泛影响其中一名pi教授研究生课程高速网络的建模和控制（ECE 459）。这个项目的成果将被纳入该课程。我们有雇佣本科生从事网络设计和控制领域的研究项目的经验。如果这个项目得到资助，我们将继续这样做。该项目开发的算法将在协调科学实验室的互联网实验室实施，并由其中一名pi指导。在过去的四年中，我们为来自工程领域代表性不足的群体的六名研究生和两名博士后研究助理提供了建议。我们将继续努力招收弱势群体的学生攻读研究生。其中一名pi在通用工程系教授本科课程。传统上，与其他工程部门相比，这个部门的本科生中女性的比例很高。通过将这个项目的一些成果纳入通用工程的本科课程，我们希望激发这个小组学生对这一领域的兴趣。p - 1

Control-Theoretic Methods for the Analysis and Design ofHigh-Speed NetworksCarolyn Beck and R. SrikantOver the last few years, a significant amount of research activity in networking has been devoted to thestudy of congestion control in the Internet. New algorithms have been suggested for congestion controllersat the sources and active queue management at the routers. While the success of the mathematical modellingapproach to congestion control has been quite remarkable, many important problems remain open. In thisproposal, we have targeted a few of these problems which have a control-theoretic flavor and therefore, webelieve, 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 resultin a loss-free, delay-free Internet, thus enabling the users of the Internet to enjoy levels of quality of ser-vicethat are not seen today. Further, our work will lay the groundwork for future Internet algorithms whenthe 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-marilyaddress the fact that today's TCP is not scalably stable. On the other hand, our work will not onlyaddress scalable stability, it also aims to improve the quality of service seen by Internet users by essentiallyeliminating 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-agementalgorithms for the Internet with a fixed number of sources, and robustness of these algorithms in thespecial case of a link accessed by many sources. While we have only scratched the surface of this rich classof 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 issuesin a broader context. Specifically, we would like to know whether we can establish the global stability ofthese algorithms for general topology networks, quantify their robustness to worst-case disturbance as wellas 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 experiencewith 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 thisproject will be implemented in Internet lab, housed in the Coordinated Science lab and directed by one ofthe PIs. Over the past four years, we have advised six graduate students and two post-doctoral researchassociates from under-represented groups in engineering. We will continue our efforts to recruit studentsfrom under-represented groups for graduate studies. One of the PIs teaches undergraduate courses in theDepartment of General Engineering. Traditionally, this department has a high percentage of women in theundergraduate population compared to other engineering departments. By incorporating some of the resultsof this project in the undergraduate courses in General Engineering, we hope to stimulate interest in thisarea among students from this group.P-1