AIMD Dynamics and Distributed Resource Allocation

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.

• Chapter 1: Origins and Applications of AIMDPart I: Linear AIMDChapter 2: Synchronized Homogeneous AIMDChapter 3: Nonsynchronized Nonhomogeneous AIMDChapter 4: The IID AIMD ModelChapter 5: Mathematical Background for Part IPart II: Stochastic Linear AIMD;Chapter 6: IID AIMD and ErgodicityChapter 7: AIMD with State-Dependent Transition ProbabilitiesChapter 8: A Markov Chain Model for Capacity EventsChapter 9: Mathematical Background for Part IIPart III: Nonlinear AIMDChapter 10: A Primer on Nonlinear AIMDChapter 11: Synchronized Homogeneous Nonlinear AIMDChapter 12: Nonsynchronized Nonhomogeneous NAIMDChapter 13: Nonsynchronized Algorithms with Stochastic State-Dependent Growth RatesPart IV: Applications of AIMD AlgorithmsChapter 14: Three Sample Applications of AIMDChapter 15: Another Application: Network Utility OptimizationChapter 16: Mathematical Background for Part IVBibliographyIndex.