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Numerical Methods for Structured Markov Chains (Hardcover, New)
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Numerical Methods for Structured Markov Chains (Hardcover, New)
Series: Numerical Mathematics and Scientific Computation
Expected to ship within 12 - 17 working days
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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.
General
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