Introduction to the Numerical Solution of Markov Chains - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to the Numerical Solution of Markov Chains write by William J. Stewart. This book was released on 2021-01-12. Introduction to the Numerical Solution of Markov Chains available in PDF, EPUB and Kindle. A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse--and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field. Here Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing methods--direct, single-and multi-vector iterative, and projection methods. More specifically, he considers recursive methods often used when the structure of the Markov chain is upper Hessenberg, iterative aggregation/disaggregation methods that are particularly appropriate when it is NCD (nearly completely decomposable), and reduced schemes for cases in which the chain is periodic. There are chapters on methods for computing transient solutions, on stochastic automata networks, and, finally, on currently available software. Throughout Stewart draws on numerous examples and comparisons among the methods he so thoroughly explains.
Numerical Methods for Structured Markov Chains
Numerical Methods for Structured Markov Chains - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Methods for Structured Markov Chains write by Dario A. Bini. This book was released on 2005-02-03. Numerical Methods for Structured Markov Chains available in PDF, EPUB and Kindle. Intersecting two large research areas - numerical analysis and applied probability/queuing theory - this book is a self-contained introduction to the numerical solution of structured Markov chains, which have a wide applicability in queuing theory and stochastic modeling and include M/G/1 and GI/M/1-type Markov chain, quasi-birth-death processes, non-skip free queues and tree-like stochastic processes. Written for applied probabilists and numerical analysts, but accessible toengineers and scientists working on telecommunications and evaluation of computer systems performances, it provides a systematic treatment of the theory and algorithms for important families of structured Markov chains and a thorough overview of the current literature.The book, consisting of nine Chapters, is presented in three parts. Part 1 covers a basic description of the fundamental concepts related to Markov chains, a systematic treatment of the structure matrix tools, including finite Toeplitz matrices, displacement operators, FFT, and the infinite block Toeplitz matrices, their relationship with matrix power series and the fundamental problems of solving matrix equations and computing canonical factorizations. Part 2 deals with the description andanalysis of structure Markov chains and includes M/G/1, quasi-birth-death processes, non-skip-free queues and tree-like processes. Part 3 covers solution algorithms where new convergence and applicability results are proved. Each chapter ends with bibliographic notes for further reading, and the bookends with an appendix collecting the main general concepts and results used in the book, a list of the main annotations and algorithms used in the book, and an extensive index.
Numerical Solution of Markov Chains
Numerical Solution of Markov Chains - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Solution of Markov Chains write by William J. Stewart. This book was released on 1991-05-23. Numerical Solution of Markov Chains available in PDF, EPUB and Kindle. Papers presented at a workshop held January 1990 (location unspecified) cover just about all aspects of solving Markov models numerically. There are papers on matrix generation techniques and generalized stochastic Petri nets; the computation of stationary distributions, including aggregation/disagg
Computations with Markov Chains
Computations with Markov Chains - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computations with Markov Chains write by William J. Stewart. This book was released on 2012-12-06. Computations with Markov Chains available in PDF, EPUB and Kindle. Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.
Numerical Solution of Markov Chains
Numerical Solution of Markov Chains - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Solution of Markov Chains write by WJ Stewart (ed). This book was released on 1991. Numerical Solution of Markov Chains available in PDF, EPUB and Kindle.
