Fundamentals of Queuing Networks : Performance, Asymptotics, and Optimization

The objective of this book is to collect in a single volume the essentials of stochastic networks, from the classical product-form theory to the more re­ cent developments such as diffusion and fluid limits, stochastic comparisons, stability, control (dynamic scheduling) and optimization. The selection of materials inevitably is a reflection upon our bias and preference, but it is also driven to a large extent by our desire to provide a graduate-level text that is well balanced in breadth and depth, suitable for the classroom. Given the wide-ranging applications of stochastic networks in recent years, from supply chains to telecommunications, it is also our hope that the book will serve as a useful reference for researchers and students alike in these diverse fields. The book consists of three parts. The first part, Chapters 1 through 4, covers (continuous-time) Markov-chain models, including the classical Jackson and Kelly networks, the notion of quasi-reversible queues, and stochastic comparisons. The second part, Chapters 5 through 10, focuses on Brownian models, including limit theorems for generalized Jackson net­ works and multiclass feedforward networks, an in-depth examination of stability in a Kumar-Seidman network, and Brownian approximations for general multiclass networks with a mixture of priority and first-in-first-out disciplines. The third part, Chapters 11 and 12, discusses scheduling in both queueing (stochastic) and fluid (deterministic) networks, along with topics such as conservation laws, polymatroid optimization, and linear pro­ gramming.

From the reviews:

SIAM REVIEW

"To summarize, this text gives well-organized and clearly written introduction to stochastic networks, as well as a complete description of some aspects of current work on these problems. It will probably appeal more to mathematicians than to engineers, especially ones interested in the theoretical aspects of diffusion and fluid approximations to complicated queuing networks. Where possible, the authors illustrate the basic concepts on a simpler form of the model, and the exercises are well chosen. The text is quite free of errors."

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

"The book attains the authors’ goal of producing a systematic exposition of the essentials of the theory of queuing networks...It is an excellent reference, well organized and clearly exposited."

"The Focus of Fundamentals of Queuing Networks (FQN) is on queuing networks. Both authors ... are leading researchers in this field. ... they manage to explain all the essential results in a sufficient amount of detail. ... FQN is designed to be a textbook, and I think, the authors have been successful on that. ... this book seems to be the most accessible one for students." (Bert Zwart, Operations Research Letters, Vol. 33, 2005)

"The book stems essentially from the lecture notes which where accumulated over many years of teaching graduate-level courses on stochastic networks by the authors ... . Its main objective is to collect, in one single-volume, the essentials of stochastic networks. ... this book is intended also to serve as a useful reference for teachers, researchers, and students alike in many of these diverse fields." (H. M. Srivastava, MathSciNet, April, 2004)

"The book attains the author’s goal of producing a systematic exposition of the essentials of the theory of queuing networks. Starting from Jackson networks, it weaves in essential threads of the theory ... . It is an excellent reference, well organized and clearly exposited." (Alan F. Karr, Journal of the American Statistical Association, December, 2002)

"This book treats stochastic networks and includes both classical results on product form networks as well as more recent work on diffusion and fluid limits, control, and optimization. The book is intended for graduate students in engineering, business, applied mathematics, and probability and statistics. ... this text gives a well-organized and clearly written introduction to stochastic networks ... . Where possible, the authors illustrate the basic concepts on a simpler form of the model, and the exercises are well chosen." (Charles Knessl, SIAM-Review, Vol. 44 (3), 2002)

"Written by two leading researchers in the field of applied probability, this text covers a breadth of material on queuing networks. ... I like the book. It is well written in a clear lucid style with key references provided at the end of each chapter. ... For researchers in the field it provides a useful compendium of results and techniques – a superb resource book that should be in the library of such applied probabilists." (Jeffrey J. Hunter, New Zealand Mathematical Society Newsletter, Issue 82, 2002)