The Mathematics of Internet Congestion Control

Congestion control algorithms were implemented for the Internet nearly two decades ago, but mathematical models of congestion control in such a large-scale network are relatively new. This text presents models for the development of new protocols that can help make Internet data transfers virtually loss- and delay-free. Introduced are tools from optimization, control theory, and stochastic processes integral to the study of congestion control algorithms.

Intended for graduate students and researchers in systems theory and computer science, the text assumes basic knowledge of first-year, graduate-level control theory, optimization, and stochastic processes, but the key prerequisites are summarized in an appendix for quick reference. The work's wide range of applications to the study of both new and existing protocols and control algorithms make the book of interest to researchers and students concerned with many aspects of large-scale information flow on the Internet.

• Approximation
• Internet
• Law of large numbers
• Routing
• Stochastic processes
• algorithms
• bridge
• information
• linear optimization
• optimization
• stochastic process
• systems theory

"This first book on the mathematics of congestion control [is] very useful for both students and researchers, but also for system engineers developing new Internet protocols. This is an elementary book for graduate students that uses a rich pallet of mathematical tools: convex optimization and control theory (Lyapunov stability and Nyquist criteria and stochastic processes). The tools are summarized well in appendices which makes the book self-contained and easy to read. The book is very well written and will undoubtedly remain a major reference on the topic for years to come."   —Mathematical Reviews

"This well-written book presents an overview of the mathematics behind internet congestion control. Focusing on the well-established TCP protocol, it starts with a gentle introduction on TCP and the packet/acknowledgement structure of the internet, before proceeding to congestion and the principles of congestion control…. Overall, this book presents in an easy-to-understand way the principles of internet congestion control with a focus on the mathematical concepts behind them. The book concludes with a useful index and a rich source of bibliographical references."   —Zentralblatt Math

"The investigation of fairness, efficiency, and dynamics of TCP led to the development of a new fast-growing research domain of mathematical models for congestion control. The Mathematics of Internet Congestion Control by R. Srikant provides a valuable comprehensive introduction to this new exciting research area. …Using mathematical models, Srikant successfully explains the principal ideas behind Internet congestion control. The publication of the book is very timely. Currently, there are no other books on mathematical models for congestion control.

…All material in the book is accessible to graduate or even undergraduate students of mathematical and electrical engineeringdisciplines. Many chapters are supplied with appendices which review the necessary background material and make the book self-contained. In conclusion, this book can be equally recommended for beginners as well as for expert researchers working in the domain of congestion control. For beginners, the book will be a good starting point from which to explore a vast and rapidly growing body of literature on the subject of Internet congestion control. For expert researchers, the book will definitely help to place congestion control in perspective and will point to new avenues in this exciting research domain." —SIAM Book Reviews

• Coordinated Science Laboratory and Department of General Engineering, University of Illinois, Urbana, USA

  R. Srikant

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