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Zusatztext '...this is an excellent book' SIAM Review, Vol.49 No.1 pp.123-176 Informationen zum Autor Dario A. Bini: Associate Editor of SIAM Journal on Matrix Analysis and Applications Member of the Editorial Board of the journal Calcolo by Springer VerlagGuy Latouche: Associate Editor of Advances in Performance AnalysisBeatrice Meini: Member of the Editorial Board of the journal Stochastic Models, Marcel Dekker Klappentext Intersecting two large research areas--numerical analysis and applied probability/quering theory--this book is a self -contained introduction to the numerical solution of structured Markov chains, which have a wide applicability in queueing theory and stochastic modeling. Aimed at graduatesand researchers in numerical analysis, applied mathematics, probability, engineering and computer science it provides 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 conceptsrelated 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 cancomputing canonical factorizations. Part 2 deals with the description and analysis of structure Markov chains and includes M/G/1, quasi-birth0death processes, non-skip-free queries and tree-like processes. Part 3 covers solution algorithms where new convergence and applicability results areproved. Each chapter ends with bibliographic notes for further reading, and the book ends 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. Zusammenfassung Intersecting two large research areas - numerical analysis and applied probability/queuing theory - this book is an introduction to the numerical solution of structured Markov chains, which have a wide applicability in queueing theory and stochastic modelling. It provides a systematic treatment of the important families of these chains. Inhaltsverzeichnis TOOLS Introduction to Markov chains Structured matrix analysis Matrix equations and canonical factorization STRUCTURED MARKOV CHAINS M/G/1-type Markov chains Phase-type queues ALGORITHMS Functional iterations Logarithmic reduction and cyclic reduction Alternative approaches Specialized structures Appendix Notations List of Algorithms Bibliography ...
