AIMD Dynamics and Distributed Resource Allocation

The AIMD algorithm is the most widely used method for allocating a limited resource among competing agents without centralised control. In this first comprehensive book on the topic, the authors offer a new approach based on positive switched linear systems, which is used to develop most of the main results in the book. Students and researchers alike will benefit from details of several variants of the algorithm, provided 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.

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.