Overview
- Presents a comprehensive methodology for the performance optimization of time-nonhomogeneous Markov chains
- Introduces the concept of confluencity, showing how it is fundamental to performance optimization and state classification
- Tackles various long-standing issues related to time-nonhomogeneous Markov chains.
- Motivates new research ideas future work in Markov system optimization
Part of the book series: SpringerBriefs in Electrical and Computer Engineering (BRIEFSELECTRIC)
Part of the book sub series: SpringerBriefs in Control, Automation and Robotics (BRIEFSCONTROL)
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Table of contents (5 chapters)
Keywords
About this book
This Springer brief addresses the challenges encountered in the study of the optimization of time-nonhomogeneous Markov chains. It develops new insights and new methodologies for systems in which concepts such as stationarity, ergodicity, periodicity and connectivity do not apply.
This brief introduces the novel concept of confluencity and applies a relative optimization approach. It develops a comprehensive theory for optimization of the long-run average of time-nonhomogeneous Markov chains. The book shows that confluencity is the most fundamental concept in optimization, and that relative optimization is more suitable for treating the systems under consideration than standard ideas of dynamic programming. Using confluencity and relative optimization, the author classifies states as confluent or branching and shows how the under-selectivity issue of the long-run average can be easily addressed, multi-class optimization implemented, and Nth biases and Blackwell optimality conditions derived. These results are presented in a book for the first time and so may enhance the understanding of optimization and motivate new research ideas in the area.
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Authors and Affiliations
About the author
Professor Xi-Ren Cao gained his B.S. in 1967 from the University of Sciences and Technology of China, and his M.S. and Ph.D. from Harvard University, in 1982 and 1984, respectively. He has worked in numerous industrial, teaching, and research positions since then, and is now a Professor Emeritus, The Hong Kong University of Science and Technology. He has acted as an Industry Consultant, was Editor-in-Chief of Discrete Event Dynamic Systems: Theory and Applications for 9 years, and is a Fellow of IFAC and the IEEE. He has published 125 peer-reviewed journal papers, 12 invited book chapters, and four books.
Bibliographic Information
Book Title: Foundations of Average-Cost Nonhomogeneous Controlled Markov Chains
Authors: Xi-Ren Cao
Series Title: SpringerBriefs in Electrical and Computer Engineering
DOI: https://doi.org/10.1007/978-3-030-56678-4
Publisher: Springer Cham
eBook Packages: Intelligent Technologies and Robotics, Intelligent Technologies and Robotics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Softcover ISBN: 978-3-030-56677-7Published: 10 September 2020
eBook ISBN: 978-3-030-56678-4Published: 09 September 2020
Series ISSN: 2191-8112
Series E-ISSN: 2191-8120
Edition Number: 1
Number of Pages: VIII, 120
Number of Illustrations: 33 b/w illustrations, 3 illustrations in colour
Topics: Control and Systems Theory, Statistics and Computing/Statistics Programs, Probability Theory and Stochastic Processes, Optimization