Probability and Statistics with Reliability , Queuing and Computer Science Applications

 (2nd 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:.

  1. Introduction
  2. Discrete Random Variables
  3. Continuous Random Variables
  4. Expectation
  5. Conditional Distribution and Expectation
  6. Stochastic Processes
  7. Discreter Time Markov Chains
  8. Continuous Time Markov Chains
  9. Networks of Queues
  10. Statistical Inference
  11. Regression and Analysis of Variance
  12.  

There are five appendices:

    1. Bibliography

B.    Property of Distributions

    1. Statistical Tables
    2. Laplace Transform
    3. Program Performance Analysis

 

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