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The state of the art in fluid-based methods for stability analysis, giving researchers and graduate students command of the tools.
List of contents
1. Introduction; 2. Stochastic processing networks; 3. Markov representations; 4. Extensions and complements; 5. Is stability achievable?; 6. Fluid limits, fluid equations and positive recurrence; 7. Fluid equations that characterize specific policies; 8. Proving fluid model stability using Lyapunov functions; 9. Max-weight and back-pressure control; 10. Proportionally fair resource allocation; 11. Task allocation in server farms; 12. Multi-hop packet networks; Appendix A. Selected topics in real analysis; Appendix B. Selected topics in probability; Appendix C. Discrete-time Markov chains; Appendix D. Continuous-time Markov chains and phase-type distributions; Appendix E. Markovian arrival processes; Appendix F. Convergent square matrices.
About the author
Jim Dai received his PhD in mathematics from Stanford University. He is currently Presidential Chair Professor in the Institute for Data and Decision Analytics at The Chinese University of Hong Kong, Shenzhen. He is also the Leon C. Welch Professor of Engineering in the School of Operations Research and Information Engineering at Cornell University. He was honored by the Applied Probability Society of INFORMS with its Erlang Prize (1998) and with two Best Publication Awards (1997 and 2017). In 2018 he received The Achievement Award from ACM SIGMETRICS. Professor Dai served as Editor-In-Chief of Mathematics of Operations Research from 2012 to 2018.J. Michael Harrison earned degrees in industrial engineering and operations research before joining the faculty of Stanford University's Graduate School of Business, where he served for 43 years. His research concerns stochastic models in business and engineering, including mathematical finance and processing network theory. His previous books include Brownian Models of Performance and Control (2013). Professor Harrison has been honored by INFORMS with its Expository Writing Award (1998), the Lanchester Prize for best research publication (2001), and the John von Neumann Theory Prize (2004); he was elected to the U.S. National Academy of Engineering in 2008.
Summary
This compact and highly readable book presents a general class of stochastic network models to develop a fluid-based method for stability analysis. Geared toward researchers and graduate students in engineering and applied mathematics, applications include back-pressure control, fair resource allocation, data center operations, and packet networks.
