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AIMD Dynamics and Distributed Resource Allocation (Advances in Design and Control)

ISBN: 9781611974218
Publisher: SIAM-Society for Industrial and Applied Mathematics
Publication Date: 2016-02-09
Number of pages: 249
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This is the first comprehensive book on the AIMD algorithm, the most widely used method for allocating a limited resource among competing agents without centralized control. The authors offer a new approach that is based on positive switched linear systems. It is used to develop most of the main results found in the book, and fundamental results on stochastic switched nonnegative and consensus systems are derived to obtain these results.

The original and best known application of the algorithm is in the context of congestion control and resource allocation on the Internet, and readers will find details of several variants of the algorithm in order of increasing complexity, including deterministic, random, linear, and nonlinear versions. In each case, stability and convergence results are derived based on unifying principles. Basic and fundamental properties of the algorithm are described, examples are used to illustrate the richness of the resulting dynamical systems, and applications are provided to show how the algorithm can be used in the context of smart cities, intelligent transportation systems, and the smart grid.

Audience: The book is suitable for advanced undergraduate and graduate students and researchers.

Contents: Chapter 1: Origins and Applications of AIMD; Part I: Linear AIMD; Chapter 2: Synchronized Homogeneous AIMD; Chapter 3: Nonsynchronized Nonhomogeneous AIMD; Chapter 4: The IID AIMD Model; Chapter 5: Mathematical Background for Part I; Part II: Stochastic Linear AIMD; Chapter 6: IID AIMD and Ergodicity; Chapter 7: AIMD with State-Dependent Transition Probabilities; Chapter 8: A Markov Chain Model for Capacity Events; Chapter 9: Mathematical Background for Part II; Part III: Nonlinear AIMD; Chapter 10: A Primer on Nonlinear AIMD; Chapter 11: Synchronized Homogeneous Nonlinear AIMD; Chapter 12: Nonsynchronized Nonhomogeneous NAIMD; Chapter 13: Nonsynchronized Algorithms with Stochastic State-Dependent Growth Rates; Part IV: Applications of AIMD Algorithms; Chapter 14: Three Sample Applications of AIMD; Chapter 15: Another Application: Network Utility Optimization; Chapter 16: Mathematical Background for Part IV; Bibliography; Index.

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