Applied Probability and Queues

Soeren Asmussen

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English

Springer Verlag
01 June 2003

Mathematics & Sciences; Probability & statistics

Series: Stochastic Modelling and Applied Probability

This book serves as an introduction to queuing theory and provides a thorough treatment of tools like Markov processes, renewal theory, random walks, Levy processes, matrix-analytic methods and change of measure. It also treats in detail basic structures like GI/G/1 and GI/G/s queues, Markov-modulated models and queuing networks, and gives an introduction to areas such as storage, inventory, and insurance risk. Exercises are included and a survey of mathematical prerequisites is given in an appendix This much updated and expanded second edition of the 1987 original contains an extended treatment of queuing networks and matrix-analytic methods as well as additional topics like Poisson's equation, the fundamental matrix, insensitivity, rare events and extreme values for regenerative processes, Palm theory, rate conservation, Levy processes, reflection, Skorokhod problems, Loynes' lemma, Siegmund duality, light traffic, heavy tails, the Ross conjecture and ordering, and finite buffer problems. Students and researchers in statistics, probability theory, operations research, and industrial engineering will find this book useful.

By: Soeren Asmussen
Imprint: Springer Verlag
Country of Publication: United States
Edition: 2nd Revised edition
Volume: v.51
Dimensions: Height: 234mm, Width: 156mm, Spine: 25mm
Weight: 1.810kg
ISBN: 9780387002118
ISBN 10: 0387002111
Series: Stochastic Modelling and Applied Probability
Pages: 450
Publication Date: 01 June 2003
Audience: General/trade , College/higher education , ELT Advanced , A / AS level
Format: Hardback
Publisher's Status: Active

Simple Markovian Models.- Markov Chains.- Markov Jump Processes.- Queueing Theory at the Markovian Level.- Queueing Networks and Insensitivity.- Some General Tools and Methods.- Renewal Theory.- Regenerative Processes.- Further Topics in Renewal Theory and Regenerative Processes.- Random Walks.- Lévy Processes, Reflection and Duality.- Special Models and Methods.- Steady-State Properties of of GI/G/1.- Markov Additive Models.- Many-Server Queues.- Exponential Change of Measure.- Dams, Inventories and Insurance Risk.

Reviews for Applied Probability and Queues

From the reviews: The author has substantially extended and updated the material to reflect developments over the period. ... The book is mainly aimed at academics and researchers, but should appeal to a wider audience of practitioners using applied probability models ... . there is much for the less well-equipped reader to enjoy and profit from. ... I would rate it as essential for any library ... and I can happily recommend it, especially to young researchers starting out in the field. (S Collins, Journal of the Operational Research Society, Vol. 56, 2005) From the reviews of the second edition: This book gives an introduction into the mathematics of queueing theory and some related fields like renewal theory on a graduate level. ... This second edition incorporates additional material ... . The book is highly recommendable to graduate students having a thorough background in probability theory. (Ulrich Horst, Zentralblatt MATH, Vol. 1029, 2004) From the reviews of the second edition: This book is a highly recommendable survey of mathematical tools and results in applied probability with special emphasis on queueing theory. ... The second edition at hand is a thoroughly updated and considerably expended version of the first edition ... . This book and the way the various topics are balanced are a welcome addition to the literature. It is an indispensable source of information for both advanced graduate students and researchers in applied probability. (Jozef L. Teugels, Mathematical Reviews, 2004f) Asmussen's book consists of 14 chapters, which are roughly divided into three parts. Each chapter contains an incredible amount of information. ... Asmussen succeeds to discuss the essentials ... and still manages to find room for a set of exercises at the end of each section. ... each section contains various useful notes and pointers to the literature. The bibliography is more than impressive. ... This makes APQ the major reference in applied probability. ... is definitely indispensable for researchers in applied probability. (Bert Zwart, Operations Research Letters, Vol. 33, 2005) The present book has been written for the advanced reader ... who is interested in a comprehensive treatment of queueing theory and related topics. This second edition contains a number of additional topics ... . At the end of almost all chapters some problems and notes on further reading are given. ... this book is an extensive and carefully written treatise on all aspects of the mathematics of queueing theory and related areas which serves both as a textbook and a reference ... . (Kirsten Henken, Operations Research - Spectrum, Issue 27, 2005) This book, which focuses mainly on queueing theory and the basic structures ... will be a valuable resource to all those interested in applied probability and stochastic modelling. It provides a clear and careful unified treatment of traditional queueing theory ... . The material is self-contained ... . Researchers and graduate students interested in these fields will no doubt want to acquire this book. (S. Drekic, Short Book Reviews, Vol. 23 (3), 2003)