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

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.

Table of 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.

About the Author :
M. Corless is a Professor in the School of Aeronautics and Astronautics at Purdue University, a Visiting Professor at University College Dublin, and an Adjunct Honorary Professor at the National University of Ireland, Maynooth. He has held a visiting position at IBM Research Ireland and is the recipient of an NSF Presidential Young Investigator Award. His research is concerned with obtaining tools that are useful in the robust analysis and control of systems containing significant uncertainty, and in applying these tools in a variety of situations. C. King is a Professor in the Mathematics Department at Northeastern University. He previously held positions at Princeton and Cornell Universities and visiting positions at ETH Zurich, Microsoft Research, and the Hamilton Institute at the National University of Ireland, Maynooth. He is a Fellow of the American Mathematical Society. His research interests include dynamical systems, quantum information theory, and mathematical physics. R. Shorten is a Professor of Control Engineering and Decision Science at University College Dublin. He is a co-founder of, and former Professor at, the Hamilton Institute at the National University of Ireland, Maynooth. He has also held a Visiting Professor position at TU Berlin, and a Senior Manager position at IBM Research Ireland, where he led the Control and Optimization activities in the area of Smart Cities. He has been active in computer networking, automotive research, collaborative mobility (including smart transportation and electric vehicles), and basic control theory and linear algebra. His main field of theoretical research is hybrid dynamical systems and stability theory for linear time-varying systems. F. Wirth is the Chair for Dynamical Systems at the University of Passau. He has held positions at the Centre Automatique et Systèmes at École des Mines de Paris, the University of Bremen, the University of Frankfurt, the University of Würzburg, the Hamilton Institute at the National University of Ireland, Maynooth, and IBM Research Ireland. He is interested in the various guises of stability properties of dynamical systems and their applications.