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Fundamentals of Matrix-Analytic Methods targets advanced-level students in mathematics, engineering and computer science. It focuses on the fundamental parts of Matrix-Analytic Methods, Phase-Type Distributions, Markovian arrival processes and Structured Markov chains and matrix geometric solutions.
New materials and techniques are presented for the first time in research and engineering design. This book emphasizes stochastic modeling by offering probabilistic interpretation and constructive proofs for Matrix-Analytic Methods. Such an approach is especially useful for engineering analysis and design. Exercises and examples are provided throughout the book.
List of contents
From Exponential Distribution to Phase-Type Distribution.- From Poisson Process to Markovian Arrival Process.- From Birth-and-Death Process to Structured Markov Chain.- Applications in Queueing Theory.- Applications in Inventory and Supply Chain Management.
Summary
Fundamentals of Matrix-Analytic Methods targets advanced-level students in mathematics, engineering and computer science. It focuses on the fundamental parts of Matrix-Analytic Methods, Phase-Type Distributions, Markovian arrival processes and Structured Markov chains and matrix geometric solutions.
New materials and techniques are presented for the first time in research and engineering design. This book emphasizes stochastic modeling by offering probabilistic interpretation and constructive proofs for Matrix-Analytic Methods. Such an approach is especially useful for engineering analysis and design. Exercises and examples are provided throughout the book.
Additional text
From the book reviews:
“This book is a graduate textbook on matrix-analytic methods. It contains many examples and exercises and should be easily accessible to graduate students. … it serves well not only as an introduction to matrix-analytic methods but also to prepare research students for dealing with open problems.” (Lothar Breuer, Mathematical Reviews, June, 2014)
“The book under review is conceived to cover three fundamental aspects of matrix-analytic methods and two of their important application areas. … The book contains a large number of exercises, some of them being given for readers to review basic calculus, linear algebra, probability theory and matrix theory. … I consider this book as a useful and instructive source for those who are interested in topics related to matrix-analytic methods.” (Gabriel V. Orman, zbMATH, Vol. 1278, 2014)
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From the book reviews:
"This book is a graduate textbook on matrix-analytic methods. It contains many examples and exercises and should be easily accessible to graduate students. ... it serves well not only as an introduction to matrix-analytic methods but also to prepare research students for dealing with open problems." (Lothar Breuer, Mathematical Reviews, June, 2014)
"The book under review is conceived to cover three fundamental aspects of matrix-analytic methods and two of their important application areas. ... The book contains a large number of exercises, some of them being given for readers to review basic calculus, linear algebra, probability theory and matrix theory. ... I consider this book as a useful and instructive source for those who are interested in topics related to matrix-analytic methods." (Gabriel V. Orman, zbMATH, Vol. 1278, 2014)
