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Reviewer: Robert B. Cooper

The first volume of this two-volume set is intended to survey the underlying theory, while the second has a more applied flavor. The books, which are similar in organization and style, complement each other, but can be used independently. In both books, each chapter begins with an abstract and a table of contents, followed by the main discussion, some thoughts about open problems or future directions, and a bibliography. The writing style and editorial conventions of both books are uniform throughout, and the chapters are further tied together via a book-wide index. The overall editing and production are excellent. Advances in queueing consists of 19 chapters written by 25 eminent researchers. The introductory chapter, “An Anthology of Classical Queueing Methods,” compiled by the editor, contains a large bibliography divided into six sections: “Special References” (15 items); “Books on Queueing Theory” (181 items); “Books on Performance Evaluation of Computer Systems, Communication Networks and Teletraffic Engineering” (234 items); “Books on Other Topics Related to Queueing” (74 items); “Surveys and Papers of Historical Interest” (116 items); and “Special Issues” (4 items). While the lists of items in each section are necessarily incomplete and reflect the tastes of the editor, the list of books on queueing theory is particularly interesting, containing almost every published English-language book with the word “queue” or one of its derivatives in the title and spanning the spectrum from famous to obscure. Also included are many books written in Russian, German, and Japanese. (I could identify only two English-language books with “queueing” in the title not included here.) The remaining 18 chapters are divided into three parts. Part 1, “Stochastic Methods,” includes the following chapters: “Queueing Methods in the Theory of Random Graphs,” by Lajos Takacs; “Stationary Distributions via First Passage Times,” by Soren Asmussen; “An Introduction to Spatial Queues,” by Erhan Cinlar; “Sample-Path Techniques in Queueing Theory,” by Shaler Stidham, Jr., and Muhammad El-Taha; “Markov-Additive Processes of Arrivals,” by Antonio Pacheco and N. U. Prabhu; “The ASTA Property,” by Benjamin Melamed and David D. Yao; “Campbells Formula and Applications to Queueing,” by Volker Schmidt and Richard F. Serfozo; and “Excess Level Processes in Queueing,” by Dshalalow. Part 2, “Analytic Methods,” contains the following chapters: “Matrix-Analytic Methods in the Theory of Queues,” by Marcel F. Neuts; “Explicit Wiener-Hopf Factorization for the Analysis of Multidimensional Queues,” by Jos H. A. de Smit; “Applications of Singular Perturbation Methods in Queueing,” by Charles Knessl and Charles Tier; “The Spectral Expansion Solution Method for Markov Processes on Lattice Strips,” by Isi Mitrani; “Applications of Vector Riemann Boundary Value Problems to Analysis of Queueing Systems,” by Alexander Dukhovny; “Light-Traffic Approximations in Queues and Related Stochastic Models,” by Bartlomiej Blaszczyszyn, Tomasz Rolski, and Volker Schmidt; “Quantitative Estimates in Queueing,” by Vladimir V. Kalashnikov; “Steady State Rare Events Simulation in Queueing Models and Its Complexity Properties,” by Soren Asmussen and Reuven Y. Rubinstein; “Piecewise-Linear Diffusion Processes,” by Sid Browne and Ward Whitt; and “Approximations of Queues via Small Parameter Method,” by Igor N. Kovalenko. An index is included at the end of the book. There are many books on queueing theory, but I could find no other book that is directly comparable to this one. As the chapter titles demonstrate, the selection of topics seems to have been determined primarily by the choice of contributing authors, rather than vice versa. Nevertheless, these authors are all major contributors to queueing theory, and their contributions all reflect the current state of the art. In conclusion, Advances in queueing would be a welcome addition to the bookshelf of anyone with a scholarly interest in queueing theory. Although Frontiers in queueing is a natural follow-up to the more theoretical Advances in queueing , it can be read independently from the first volume. It includes a plethora of tools for the more practical reader, as well as a variety of queueing models and networks. (From the Preface) Frontiers in queueing is indeed concerned with models and applications, but I would warn any potential buyer who considers himself or herself a “practical reader” seeking tools not to be overly optimistic. Frontiers in queueing may be less theoretical than Advances in queueing , which is concerned primarily with the mathematics that underlies queueing theory, but it is equal to it in terms of the high quality of its scholarship. Like its companion volume Advances in queueing , the selection of topics in Frontiers in queueing seems to have been determined by the editors selection of contributing authors. As in the other book, these authors are all experts, and all of their contributions authoritatively reflect the current state of the art. Frontiers in queueing consists of 16 chapters written by 26 authors, who are accurately described in the books cover blurb as “internationally renowned.” The chapters are grouped into four categories. Part 1, “Progress of Classical Queueing Models,” includes the following chapters: “A Personal View of Queueing Theory,” by Ryszard Syski; “Retrial Queues Revisited,” by V. G. Kulkarni and H. M. Liang; “Some Results for the Mean Waiting-Time and Workload in GIGIk Queues,” by Daryl J. Daley; and “Queueing Systems with State-Dependent Parameters,” by Dshalalow. Part 2, “Telecommunications and Computer Networks,” consists of three chapters: “Queueing Analysis of Polling Models: Progress in 1990–1994,” by Hideaki Takagi; “Prod u ct-form Loss Networks,” by Hisashi Kobayashi and Brian L. Mark; and “Sojourn Time Distributions in Non-Product Queueing Networks,” by Hans Daduna. Part 3, “Traffic Processes,” contains the chapters “Stochastic Geometry Models of Mobile Communication Networks,” by Francois Baccelli and Serguei Zuyev; “Fractal Queueing Models,” by Ashok Erramilli, Onuttom Narayan, and Walter Willinger; “Stochastic Modeling of Traffic Processes,” by David L. Jagerman, Benjamin Melamed, and Walter Willinger; and “Fluid Models for Single Buffer Systems,” by V. G. Kulkarni. Part 4, “Applied Techniques and Statistical Inference in Queueing Models,” includes the following chapters: “Computational Methods in Queueing,” by Henk J. Tijms; “Statistical Analysis of Queueing Systems,” by U. Narayan Bhat, Gregory K. Miller, and S. Subba Rao; “Perturbation Analysis for Control and Optimization of Queueing Systems: An Overview and the State of the Art,” by Yu-Chi Ho and Christos G. Cassandras; “Polynomial Time Algorithms for Estimation of Rare Events in Queueing Models,” by Vladimir Kriman and Reuven Y. Rubinstein; and “Parametric Estimation of Tail Probabilities for the Single-Server Queue,” by Peter W. Glynn and Marcelo Torres. An index concludes the book. My only compensation for reviewing Frontiers in queueing is getting to keep the review copy. Considering that this is an excellent book, I think I got a very good deal.