Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics. The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation. Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only). * Numerous examples illuminate the mathematical theories * Carefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approach * Each chapter concludes with an extensive set of exercises

This is an excellent book on the topics of probability, Markov chains, and queuing theory. Extremely well-written, the contents range from elementary topics to quite advanced material and include plenty of well-chosen examples. -- Adarsh Sethi, University of Delaware Clear and pleasant to read, this book distinguishes itself from comparable textbooks by its inclusion of the computational aspects of the material. -- Richard R. Muntz, University of California, Los Angeles

About the Author
William J. Stewart is professor of computer science at North Carolina State University. He is the author of "An Introduction to the Numerical Solution of Markov Chains" (Princeton).

Reviews
"The book represents a valuable text for courses in statistics and stochastic processes, so it is strongly recommended to libraries."--Hassan S. Bakouch, Journal of Applied Statistics



Book Information
ISBN 9780691140629
Author William J. Stewart
Format Hardback
Page Count 776
Imprint Princeton University Press
Publisher Princeton University Press
Weight(grams) 1474g