Numerical Methods for Structured Markov Chains
Series: Numerical Mathematics and Scientific Computation;
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Product details:
- Publisher OUP Oxford
- Date of Publication 3 February 2005
- ISBN 9780198527688
- Binding Hardback
- No. of pages340 pages
- Size 242x163x23 mm
- Weight 754 g
- Language English 0
Categories
Short description:
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 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.
MoreLong description:
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 to engineers 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 and analysis 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 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.
The book is useful for researchers and PhD students both in the field of applied probability and numerical analysis, it can be used by specialists dealing with telecommunication and computer systems.
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
