Prabhu is an eminent author and researcher, and founding editor of the influential journal Queueing Systems. The content, objectives, target audience, and prerequisites for this book are best described by quoting from the preface:

Over the last twenty years several books on queueing theory have appeared, treating it at a level suitable for an undergraduate course of study. These books were adequate for their purpose for a while, but with rapid advances in the subject area their treatment has become a little outdated. This is because current research has shown the need to pay more attention to the basic concepts and techniques of queueing theory.… The present book deals with the foundations of queueing theory and is intended as a text for an undergraduate course on queueing theory. I have not attempted to merely chronicle the results of queueing theory as historically derived, but established them by my own approach to the subject.…

A pre-requisite for the book is an undergraduate course on stochastic processes. The earlier part of the text uses results from the Poisson process, renewal theory, birth-and-death processes and Markov chains. As the presentation progresses, relatively advanced concepts such as time-reversibility, vector Markov processes, Wiener-Hopf technique and regenerative sets are introduced, with strong motivation from the queueing models considered. Applied mathematical tools used in the text include generating functions, Laplace transforms, Laplace-Stieltjes transforms and Fourier transforms. It is expected that the instructor will provide a brief review of this material.

The book consists of eight chapters, an appendix, a bibliography, and an index. Each chapter includes exercises. Numerical computation and simulation studies have been omitted as beyond the scope of this text. The chapter titles are

• Introduction

• Markovian Queueing Systems

• The Busy Period, Output and Queues in Series

• Erlangian Queueing Systems

• Priority Systems

• Queueing Networks

• The System M/G/1; Priority Systems

• The System GI/G/1; Imbedded Markov Chains

The blurb on the back cover says that “the book…is intended as an advanced text for courses on queueing theory, and as a professional reference to queueing research,” but it is clear from the author’s preface that he intended it as an undergraduate text. Still, it is not clear what kind of audience this book actually targets. The results are presented in a theorem-proof format, which would appeal to an audience of mathematicians or mathematics majors. There is little discussion or interpretation of the theorems and formulas. The “Problems for Solution” that end each chapter are of two types: (a) proofs or derivations, and (b) descriptive problems that require numerical answers (which are given at the end of the problem statement). There are fewer problems of type (b), and they tend to be much simpler than those of type (a). They are barely suggestive of real applications in operations research.

The book’s organization and style seem to be motivated primarily by considerations of mathematical elegance, rather than by a desire to explain basic facts to undergraduates as simply as possible. Also, there is little discussion of PASTA (the acronym is never mentioned) and no discussion of insensitivity. I find this surprising, because these topics are of fundamental interest to mathematicians and operations researchers alike.

This book would be an interesting addition to the library of the queueing theory aficionado, but because of its idiosyncratic choice of topics and methods, I doubt that it will have wide appeal as an undergraduate text.