Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000010105524 | QA274.7 B56 2005 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
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 graduates and 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 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 can computing 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 are proved. 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.
Author Notes
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
Table of Contents
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 |