Probability
and Statistics with Reliability , Queuing and Computer Science Applications
(2^{nd} ed.) by Kishor S. Trivedi,
New York: John Wiley 2002, ISBN0-471-33341-7, xv+830 pp., $89.95.
This second edition follows 20 years after the first, and, while retaining the same number of chapters and chapter titles, has grown by more than 200 pages and made a huge leap into the present. This book is a tour de force of clear, virtually error-free exposition of probability as it is applied in a host of up-to-date contexts, such as cellular wireless communication, software reliability and stochastic Petri nets. It will richly reward the diligent reader. The book’s main emphasis and strength is probability theory. Statistical inference and regression occupy only 127 of the books 830 pages.
According to the preface to the first edition the
aim of the book is “to provide an introduction to probability, stochastic
processes and statistics for students of computer science, electrical/computer
engineering, reliability engineering, and applied mathematics. The prerequisites are two semesters of
calculus, a course on introduction to computer programming, and preferably, a
course on computer organization.” The
preface to the second edition doesn’t amend the aim or prerequisites so we
assume they stand, but it does visualize use of the book beyond the classroom
for practicing engineers and researchers.
My own feeling is that a student without some previous exposure to
probability and statistics will find the book challenging.
The
chapters are as follows:.
There
are five appendices:
Pedagogically, those weary of urns, dice and cards,
will find some new and more relevant ways of illustrating probability concepts.
For example to illustrate a Bernoulli trial Trivedi considers an IF
statement in a computer code with success defined as “then clause is
executed’ and failure defined as “else clause executed”. Sometimes the examples move swiftly from an
elementary point deep into a contemporary application in computer performance
analysis, reliability or queuing. In
the Chapter 1, to illustrate the multiplication of probabilities for
independent events, he considers computation of the system reliability for
series and parallel combinations of components with specified survival
probabilities. This is likely more
appealing to engineering students than successive coin tosses. But once on a
topic Trivedi sometimes continue further than seems consistent with the point
illustrated. For instance, the series and parallel reliability discussion is
followed by a discussion of structure functions and fault trees, topics usually
encountered in later chapters of a reliability text.
Sometimes a background in electrical engineering is needed to grasp the context in which a probabilistic concept is being illustrated. For instance Example 1.7 illustrates a hypergeometric probability calculation in a context that begins “ consider a TDMA (time division multiple access) wireless system where the base transceiver system of each cell has n base repeaters (also called base radio (BR)). Each base receiver provides m time-division-multiplexed channels…”
The book is rife with acronyms, which, once defined,
are used freely and without apology thereafter. Fortunately a codebook of three
pages just after the Preface lists the words that the acronym letters stand
for, but give no deeper explanation of their meaning. So, for example, the
reader will learn that TMR stands for triple modular redundancy, but will have
to find the point in the text where TMR is first introduced to get more of an
explanation. It is clear that the author intends the reader to proceed through
the book sequentially from start to finish.
While the book contains most, if not all, the
material typically found in a text on reliability engineering, or a text on
queuing theory, the individual topics are dispersed throughout the book,
appearing where they are germane to the scope of the chapter in which they are
found. This will foil the reader trying to use the text to master a single
application area. For example, in Chapter 7, on discrete time Markov chains, a
derivation of the Pollaczek-Khinchin transform equation of queuing theory
segues into an analysis of the flow graph of a computer program to determine
its reliability in terms of the reliability of
interconnnected groups of statements, and in Chapter 8,on continuous
time markov chains, applications to cyclic queues in multiprogramming computer
environments are juxtaposed with the analysis of the availability of systems
which undergo breakdown and repair.
My advice:
Read the book cover to cover. It’s worth the effort.
John l.
McCool
Pennsylvania
State University, Great Valley