*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*