This is a very technical book that contains a thorough treatment of the various queueing models used in the analysis of polling systems. The purpose of the book is to present the essential results obtained so far and to give the derivations of these results using mathematics that is not necessarily sophisticated. In fact, the contents of the book are essentially limited to these derivations. The reader is assumed to be familiar with polling systems, so there is no need to pose questions about the validity of problems. In the same way, no applications of the results are suggested. Practically all results are given in formulas; the study of the behavior of some real system is left to the reader. On the other hand, the book can well be read without this kind of knowledge as an interesting collection of problems in queueing theory.

The presentation is rather mathematically oriented, and the book advances through a continual derivation of subsequent formulas. Text passages are short and their purpose is merely to give the necessary short explanations. In spite of this, the book is not too difficult to read: the mental steps required from the reader are modest, and a reader accustomed to a mathematical presentation will find the derivations and proofs easy to follow. This is especially true since most of the material is based on a rather unsophisticated level of mathematical analysis and probability theory.

The basic terms used in dealing with queueing models of polling systems are briefly explained in Chapter 1. Chapter 2 presents the analysis for a continuous-time, one-message buffer system with general reply intervals. This is followed by an analysis dealing with the case of constant parameters. Chapters 3 through 5 provide a unified presentation of the analysis of infinite buffer systems with exhaustive and gated service. In Chapter 3 a detailed procedure for solving an exhaustive-service, discrete-time system is presented. The continuous-time version is dealt with in Chapter 4. Following are chapters about gated service systems, limited service systems, and systems with zero reply times. A short chapter is dedicated to applications, i.e., to models used in some special cases. The last chapter summarizes the state of the art and suggests further research topics.

The book contains an excellent survey of the results obtained in analyzing polling systems with queueing models. The essential references to the relevant literature are given, and the basic results are derived, either through reproducing earlier work or through the author’s own contribution.

Who will benefit from this book? Certainly it is not a textbook for a one-semester course in data communications or queueing theory applications. However, it is a good handbook for an analyst: it contains the known theoretical results, and it also tells what is not known. For an instructor, it tells how the basic results can be obtained using rather straightforward methods; some of this material can well be incorporated into suitable courses where performance analysis or data communications systems are considered. Overall, it is a thorough monograph on the queueing models used in the analysis of polling systems.