The Mathematics Of Internet Congestion Control

* Recommended by T.Basar, SC series ed. * This text addresses a new, active area of research and fills a gap in the literature. * Bridges mathematics, engineering, and computer science; considers stochastic and optimization aspects of congestion control in Internet data transfers. * Useful as a supplementary text & reference for grad students with some background in control theory; also suitable for researchers.

This is a print on demand edition of a hard to find publication. Society is becoming increasingly reliant on large networked information systems for commerce, communication, education, entertainment and government. Currently, however, system designers lack techniques to predict global behaviors that may arise in the Internet as a result of interactions among existing and altered software components. Hardware faults and unexpected usage patterns may also occur within the Internet. This study aims to improve existing knowledge about a range of methods and tools that could be applied to understand and predict behavior in complex information systems. Charts and tables.

As the Internet becomes increasingly heterogeneous, the issue of congestion control becomes ever more important. In order to maintain good network performance, mechanisms must be provided to prevent the network from being congested for any significant period of time. Michael Welzl describes the background and concepts of Internet congestion control, in an accessible and easily comprehensible format. Throughout the book, not just the how, but the why of complex technologies including the Transmission Control Protocol (TCP) and Active Queue Management are explained. The text also gives an overview of the state-of-the-art in congestion control research and an insight into the future. Network Congestion Control: Presents comprehensive, easy-to-read documentation on the advanced topic of congestion control without heavy maths. Aims to give a thorough understanding of the evolution of Internet congestion control: how TCP works, why it works the way it does, and why some congestion control concepts failed for the Internet. Explains the Chiu/Jain vector diagrams and introduces a new method of using these diagrams for analysis, teaching & design. Elaborates on how the theory of congestion control impacts on the practicalities of service delivery. Includes an appendix with examples/problems to assist learning. Provides an accompanying website with Java tools for teaching congestion control, as well as examples, links to code and projects/bibliography. This invaluable text will provide academics and researchers in computer science, electrical engineering and communications networking, as well as students on advanced networking and Internet courses, with a thorough understanding of the current state and future evolution of Internet congestion control. Network administrators and Internet service and applications providers will also find Network Congestion Control a comprehensive, accessible self-teach tool.

This brief proposes that the keys to internet cross-layer optimization are the development of non-standard implicit primal-dual solvers for underlying optimization problems, and design of jointly optimal network protocols as decomposition of such solvers. Relying on this novel design-space oriented approach, the author develops joint TCP congestion control and wireless-link scheduling schemes for wireless applications over Internet with centralized and distributed (multi-hop) wireless links. Different from the existing solutions, the proposed schemes can be asynchronously implemented without message passing among network nodes; thus they are readily deployed with current infrastructure. Moreover, global convergence/stability of the proposed schemes to optimal equilibrium is established using the Lyapunov method in the network fluid model. Simulation results are provided to evaluate the proposed schemes in practical networks.

Internet Congestion Control provides a description of some of the most important topics in the area of congestion control in computer networks, with special emphasis on the analytical modeling of congestion control algorithms. The field of congestion control has seen many notable advances in recent years and the purpose of this book, which is targeted towards the advanced and intermediate reader, is to inform about the most important developments in this area. The book should enable the reader to gain a good understanding of the application of congestion control theory to a number of application domains such as Data Center Networks, Video Streaming, High Speed Links and Broadband Wireless Networks. When seen through the lens of analytical modeling, there are a number of common threads that run through the design and analysis of congestion control protocols in all these different areas, which are emphasized in this book. The book also cuts a path through the profusion of algorithms in the literature, and puts the topic on a systematic and logical footing. Internet Congestion Control provides practicing network engineers and researchers with a comprehensive and accessible coverage of analytical models of congestion control algorithms, and gives readers everything needed to understand the latest developments and research in this area. Examines and synthesizes the most important developments in internet congestion control from the last 20 years. Provides detailed description on the congestion control protocols used in four key areas; broadband wireless networks, high speed networks with large latencies, video transmission networks, and data center networks. Offers accessible coverage of advanced topics such as Optimization and Control Theory as applied to congestion control systems.

Establishing adaptive control as an alternative framework to design and analyze Internet congestion controllers, End-to-End Adaptive Congestion Control in TCP/IP Networks employs a rigorously mathematical approach coupled with a lucid writing style to provide extensive background and introductory material on dynamic systems stability and neural network approximation; alongside future internet requests for congestion control architectures. Designed to operate under extreme heterogeneous, dynamic, and time-varying network conditions, the developed controllers must also handle network modeling structural uncertainties and uncontrolled traffic flows acting as external perturbations. The book also presents a parallel examination of specific adaptive congestion control, NNRC, using adaptive control and approximation theory, as well as extensions toward cooperation of NNRC with application QoS control. Features: Uses adaptive control techniques for congestion control in packet switching networks Employs a rigorously mathematical approach with lucid writing style Presents simulation experiments illustrating significant operational aspects of the method; including scalability, dynamic behavior, wireless networks, and fairness Applies to networked applications in the music industry, computers, image trading, and virtual groups by techniques such as peer-to-peer, file sharing, and internet telephony Contains working examples to highlight and clarify key attributes of the congestion control algorithms presented Drawing on the recent research efforts of the authors, the book offers numerous tables and figures to increase clarity and summarize the algorithms that implement various NNRC building blocks. Extensive simulations and comparison tests analyze its behavior and measure its performance through monitoring vital network quality metrics. Divided into three parts, the book offers a review of computer networks and congestion control, presents an adaptive congestion control framework as an alternative to optimization methods, and provides appendices related to dynamic systems through universal neural network approximators.

The congestion control mechanism has been responsible for maintaining stability as the Internet scaled up by many orders of magnitude in size, speed, traffic volume, coverage, and complexity over the last three decades. In this book, we develop a coherent theory of congestion control from the ground up to help understand and design these algorithms. We model network traffic as fluids that flow from sources to destinations and model congestion control algorithms as feedback dynamical systems. We show that the model is well defined. We characterize its equilibrium points and prove their stability. We will use several real protocols for illustration but the emphasis will be on various mathematical techniques for algorithm analysis. Specifically we are interested in four questions: 1. How are congestion control algorithms modelled? 2. Are the models well defined? 3. How are the equilibrium points of a congestion control model characterized? 4. How are the stability of these equilibrium points analyzed? For each topic, we first present analytical tools, from convex optimization, to control and dynamical systems, Lyapunov and Nyquist stability theorems, and to projection and contraction theorems. We then apply these basic tools to congestion control algorithms and rigorously prove their equilibrium and stability properties. A notable feature of this book is the careful treatment of projected dynamics that introduces discontinuity in our differential equations. Even though our development is carried out in the context of congestion control, the set of system theoretic tools employed and the process of understanding a physical system, building mathematical models, and analyzing these models for insights have a much wider applicability than to congestion control.