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Probability, Markov chains, queues, and simulation. The mathematical basis of performance modeling. (English) Zbl 1176.60003
Princeton, NJ: Princeton University Press (ISBN 978-0-691-14062-9/hbk). xviii, 758 p. (2009).
The purpose of this book is to provide the student and teachers with a modern approach for building and solving probability based models with confidence. The book is divided into four major parts, namely, “Probability”, “Markov Chains”, “Queueing Models” and “Simulation”.
Part I is self-contained and complete and should be accessible to anyone with a basic knowledge of calculus. Newcomers to probability theory as well as those whose knowledge of probability is rusty should be equally at ease in their progress through this part. Particular attention is paid to phase-type distributions due to the important role they play in modeling scenarios and the chapter also includes a section on fitting phase-type distributions to given means and variances.
Part II contains two rather long chapters on the subject of Markov chains, the first on theoretical aspects of Markov chains, and the second on their numerical solution. The advantage of this part that it deals with numerical solutions, from Gaussian elimination and basic iterative-type methods for stationary solutions to ordinary differential equation solvers for transient solutions. Block methods and iterative aggregation-disaggregation methods for nearly completely decomposable Markov chains are considered. A section is devoted to matrix geometric and matrix analytic methods for structured Markov chains. Algorithms and computational considerations are stressed throughout this chapter.
Queueing models are presented in the five chapters that constitute Part III. The final chapter treats queueing networks. Open networks are introduced via Burke’s theorem and Jackson’s extensions to this theorem. Closed queueing networks are treated using both the convolution algorithm and the mean value approach. The “flow-equivalent server” approach is also treated and its potential as an approximate solution procedure for more complex networks is explored. The chapter terminates with a discussion of product form in queueing networks and the BCMP theorem for open, closed, and mixed networks.
The final part of the text, Part IV, deals with simulation. After random number generations it concerns simulation measurement and accuracy and is based on sampling theory. Special attention is paid to the generation of confidence intervals and to variance reduction techniques, an important means of keeping the computational costs of simulation to a manageable level.
Numerous examples with detailed explanations are provided throughout the text. These examples are designed to help the student more clearly understand the theoretical and computational aspects of the material and to be in a position to apply the acquired knowledge to hisfher own areas of interest. A solution manual is available for teachers who adopt this text for their courses. This manual contains detailed explanations of the solution of all the exercises. Where appropriate, the text contains program modules written in Matlab or in the Java programming language.
This book has been designed for students from a variety of academic disciplines in which stochastic processes constitute a fundamental concept, disciplines that include not only computer science and engineering, industrial engineering, and operations research, but also mathematics, statistics, economics, and business, the social sciences-in fact all disciplines in which stochastic performance modeling plays a primary role.
In my opinion the present text book is carefully written, well-balanced and a great helf for those who teach stochastic modeling, applied probabiliy, performance modeling. My congratulations to the author.

##### MSC:
 60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory 60Gxx Stochastic processes 60K25 Queueing theory (aspects of probability theory)
##### Keywords:
performance modeling; Markov chains; queueing theory; simulation
Matlab