Stochastic Networks (Institute of Mathematical Statistics Textbooks 2)
By: Frank Kelly (author), Elena Yudovina (author)Paperback
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Communication networks underpin our modern world, and provide fascinating and challenging examples of large-scale stochastic systems. Randomness arises in communication systems at many levels: for example, the initiation and termination times of calls in a telephone network, or the statistical structure of the arrival streams of packets at routers in the Internet. How can routing, flow control and connection acceptance algorithms be designed to work well in uncertain and random environments? This compact introduction illustrates how stochastic models can be used to shed light on important issues in the design and control of communication networks. It will appeal to readers with a mathematical background wishing to understand this important area of application, and to those with an engineering background who want to grasp the underlying mathematical theory. Each chapter ends with exercises and suggestions for further reading.
Frank Kelly is Professor of the Mathematics of Systems at the University of Cambridge. His main research interests are in random processes, networks and optimization. He is especially interested in applications to the design and control of networks and to the understanding of self-regulation in large-scale systems. Elena Yudovina is a postdoctoral research fellow at the University of Michigan. Her research interests are in applications of queueing theory. She received her PhD from the University of Cambridge, where her interest in the subject was sparked by a course on stochastic networks taught by Frank Kelly.
Overview; Part I: 1. Markov chains; 2. Queueing networks; 3. Loss networks; Part II: 4. Decentralized optimization; 5. Random access networks; 6. Effective bandwidth; Part III: 7. Internet congestion control; 8. Flow level internet models; Appendix A. Continuous time Markov processes; Appendix B. Little's law; Appendix C. Lagrange multipliers; Appendix D. Foster-Lyapunov criteria; References; Index.
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- ID: 9781107691704
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