Reviewing this book is challenging because it is a research monograph in the form of a textbook. As a report of research, it is very good. It represents both theory and computation for finding optimal policies for queueing systems. There are good bibliographic reviews at the end of each chapter that give the context for the work and a critical evaluation of how it fits in with the literature. The topics are developed in a consistent, logical manner.

Chapter 1 is a general introduction that describes the organization of the book and gives some basic definitions. Chapter 2 presents additional definitions, concepts, and notation used in subsequent chapters and develops computational models for finding optimal policies when the state space is infinite. Chapters 3 and 4 develop additional models for a finite horizon (limited time) and for an infinite horizon with discounted cost, respectively. An inventory model example is treated in chapter 5, in which the ideas and formalism in the previous chapters are applied. The remaining five chapters discuss average cost optimization under different conditions: for finite state spaces, for countable state spaces, for infinite state spaces (when control can be exercised only in selected time slots) and for continuous-time processes.

Three appendices provide background information. The first is a collection of theorems from analysis; the second is on the sequences of stationary policies using topological concepts; and the third is on Markov chains. A bibliography follows the appendices. Most of the entries in the brief index refer to proper names that appear in the end-of-chapter bibliographic notes.

The material is presented as theorems and proofs. This format is much more suitable for a research monograph than for a textbook. Many of the end-of-chapter exercises emphasize proofs and derivations. Some problems ask students to use one of nine downloadable programs written in Pascal. Used as a textbook, the suggested target audience is graduate students and advanced undergraduates. For the latter, Sennott suggests that the details of the proofs be omitted and that the conclusions presented in the theorems be emphasized. I think that graduate students will find this book demanding, and undergraduates will be lost. Even the examples (such as the inventory model in chapter 5) are presented in a highly formal manner that many students will find difficult. The book is much more successful as a research report.

The publisher’s ftp site did not have the programs as of this writing (December 1998). They are downloadable in HTML format from the author’s Web site (www2.math.ilstu .edu/˜sennott/stochdynprog.html). Readers will need to strip the HTML tags from these files and reformat them for subsequent compilation.