Probability and Statistics with Reliability, Queuing, and Computer Science Applications

KISHOR SHRIDHARBHAI TRIVEDI

2nd Edition. Wiley (2002), ISBN 0-471-33341-7. £66.95/$105.90. 848 pp. Hardbound.

The first edition of this book was published two decades ago, and soon became a well-recognized classic book in the area of performance and reliability modelling and evaluation of computer and communication systems. The second edition appeared in 2002, published by Wiley. This second edition is much more than a simple updating of the previous one. A substantial amount of new material has been included for the first time, old chapters have been rewritten adopting a more advanced and powerful formalism, new and motivating examples and up-to-date case studies and problems have been added and, finally, the list of references has been considerably enriched. The book provides a comprehensive introduction to probability, statistics and stochastic processes, and leads the reader to a natural understanding of how these concepts and related methods can be applied in the modelling, analysis and quantitative evaluation of the performance and reliability of systems. The major merit of the book is that its pages

contain, in the same readable language, classic material together with recent advances and achievements distilled from the author’s research activity and experience in the area

of the modelling and evaluation of stochastic systems.

Some new topics that are covered in the book through examples and problems are still open research areas, such as performability models, software reliability, wireless system performance and availability modeling. Some consolidated topics have been inserted for the first time in the second edition, such as fault trees, numerical techniques for Markov chains, stochastic Petri nets. Moreover, some additional classical material is reconsidered in a more modern and up to date manner. Most measures are cast in the framework of Reward Stochastic Processes: the use of reward rate variables associated to stochastic systems was confined to an advanced research environment, and it is undoubtedly a merit of Professor Trivedi to have adopted this formalism in a textbook of large diffusion and to have shown how their use can contribute to a unifying formulation and computation of performance and reliability measures. Furthermore, the new edition formulates discrete and continuous Markov chains in terms of matrix equations, thus correcting what, for me, was the major drawback of the first edition.

The book consists of 11 chapters and several appendices. All the chapters are enriched with very useful and motivating examples, problems and complementary exercises (a solution manual for instructors is available from the publisher). The first five chapters provide an introduction to probability theory and can constitute the basis for a course on the subject. The largest and most significant portion of the book covers the topic of stochastic processes and their application to the modelling and analysis of the performance and dependability of systems. Chapter 6 presents an introduction and classification of stochastic processes and discusses Poisson and renewal processes with a useful addition of a section on availability analysis. Chapter 7 is devoted to discrete-time Markov chains whereas Chapter 8, perhaps the central one to the book, is devoted to continuous-time Markov chains. After introducing the basic concepts and equations, Chapter 8 discusses birth–death processes in general, and shows how queuing systems can find application in many real-life problems (repairman and availability models, telephone and wireless network capacity). Absorption problems in Markov chains are considered in a specific section, and two subsequent, completely new, sections on numerical methods and on the automated generation of Markov models by means of stochastic Petri nets complement and conclude the chapter. Chapter 9 deals with open and closed queuing networks, as well as nonproduct-form networks of queues. The last two chapters (Chapters 10 and 11) deal with statistical inference and regression, respectively, and again can be considered as basic material for an introductory course on statistics.

This is an excellent, self-contained book that can serve as a classroom textbook for a complete series of courses, starting from basic probability and statistics to advanced stochastic modelling, with emphasis on the applicative areas of performance and reliability evaluation of computer and communication systems. But the book may, as well, constitute a valuable reference book for engineers and professionals delving in the area of reliability and performance. In summary, I recommend the book to beginners and veterans in the field, and to anyone who thinks, as I do, that a fundamental knowledge in dependability methods is useful or necessary to face the complexity of modern computer and communication systems.

ANDREA BOBBIO

Universit`a del Piemonte Orientale, Italy