Fundamentals of matrix-analytic methods. (English) Zbl 1278.68013
New York, NY: Springer (ISBN 978-1-4614-7329-9/hbk; 978-1-4614-7330-5/ebook). xv, 349 p. (2014).
The book under review is conceived to cover three fundamental aspects of matrix-analytic methods and two of their important application areas. Each chapter begins with basic concepts and well-known models in stochastic processes, followed by concepts and models in matrix-analytic methods.
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. Some exercises are very simple and are intended for understanding fundamental concepts and ideas. Other exercises are typical and are intended for practicing the use of the theory developed.
Finally, some exercises are for extensions of the theory and are presented for information.
The book has 5 chapters and consists of a theoretical part and an application part.
To the theoretical part belong Chapters 1, 2 and 3, and the application part includes Chapters 4 and 5.
Chapter 1 defines the exponential distribution and, from here, introduces phase-type distributions. Chapter 2 deals with the Poisson process and, from there, introduces Markovian arrival processes. Then, Chapter 3 defines the birth-and-death process and, from there, introduces Markov chains of the QBD, GI/M/1, and M/G/1 type.
Then, Chapter 4 defines the M/M/1 queue; more complex queueing models follow that can be analyzed using matrix-analytic methods. Finally, Chapter 5 focuses on inventory and supply chain models.
I consider this book as a useful and instructive source for those who are interested in topics related to matrix-analytic methods.
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. Some exercises are very simple and are intended for understanding fundamental concepts and ideas. Other exercises are typical and are intended for practicing the use of the theory developed.
Finally, some exercises are for extensions of the theory and are presented for information.
The book has 5 chapters and consists of a theoretical part and an application part.
To the theoretical part belong Chapters 1, 2 and 3, and the application part includes Chapters 4 and 5.
Chapter 1 defines the exponential distribution and, from here, introduces phase-type distributions. Chapter 2 deals with the Poisson process and, from there, introduces Markovian arrival processes. Then, Chapter 3 defines the birth-and-death process and, from there, introduces Markov chains of the QBD, GI/M/1, and M/G/1 type.
Then, Chapter 4 defines the M/M/1 queue; more complex queueing models follow that can be analyzed using matrix-analytic methods. Finally, Chapter 5 focuses on inventory and supply chain models.
I consider this book as a useful and instructive source for those who are interested in topics related to matrix-analytic methods.
Reviewer: Gabriel V. Orman (Braşov)
MSC:
| 68-02 | Research exposition (monographs, survey articles) pertaining to computer science |
| 60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |
| 68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |
| 60K25 | Queueing theory (aspects of probability theory) |
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
