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An Introduction to Queueing Theory

and Matrix-Analytic Methods

  • Textbook
  • © 2005

Overview

Authors:
  1. L. Breuer

    1. University of Trier, Germany

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  2. D. Baum

    1. University of Trier, Germany

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  • Provides a systematic introduction to queueing theory within the framework of Markov renewal theory
  • Covers phase-type distributions, Markovian arrival processes, the GI/PH/1 and BMAP/G/1 queues as well as QBDs and discrete time approaches
  • This is the first textbook that contains an extensive presentation of matrix-analytic methods as a natural extension of classical methods
  • Concise style makes it suitable for the blueprint of a lecture script

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Queues: The Art of Modelling

    1. Queues: The Art of Modelling

      Pages 1-7

  4. Semi-Markovian Methods

    1. Renewal Theory

      Pages 113-134

    2. Markov Renewal Theory

      Pages 135-146

    3. Semi-Markovian Queues

      Pages 147-166

  5. Matrix-Analytic Methods

    1. Phase-Type Distributions

      Pages 169-184

    2. Markovian Arrival Processes

      Pages 185-196

    3. The GI/PH/1 Queue

      Pages 197-212

    4. The BMAP/G/1 Queue

      Pages 213-227

    5. Discrete Time Approaches

      Pages 229-238

    6. Spatial Markovian Arrival Processes

      Pages 239-251

    7. Appendix

      Pages 253-261

  6. Back Matter

    Pages 263-271
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Keywords

About this book

The present textbook contains the recordsof a two–semester course on que- ing theory, including an introduction to matrix–analytic methods. This course comprises four hours oflectures and two hours of exercises per week andhas been taughtattheUniversity of Trier, Germany, for about ten years in - quence. The course is directed to last year undergraduate and?rst year gr- uate students of applied probability and computer science, who have already completed an introduction to probability theory. Its purpose is to present - terial that is close enough to concrete queueing models and their applications, while providing a sound mathematical foundation for the analysis of these. Thus the goal of the present book is two–fold. On the one hand, students who are mainly interested in applications easily feel bored by elaborate mathematical questions in the theory of stochastic processes. The presentation of the mathematical foundations in our courses is chosen to cover only the necessary results,which are needed for a solid foundation of the methods of queueing analysis. Further, students oriented - wards applications expect to have a justi?cation for their mathematical efforts in terms of immediate use in queueing analysis. This is the main reason why we have decided to introduce new mathematical concepts only when they will be used in the immediate sequel. On the other hand, students of applied probability do not want any heur- tic derivations just for the sake of yielding fast results for the model at hand.

Reviews

From the reviews:

"This book provides a mathematical introduction to the theory of queuing theory and matrix-analytic methods … . The style of the text … is concise and rigorous. The proofs are presented for study. Each chapter concludes with a set of exercises inviting readers to prove supplementary results and review particular aspects of the theory. … I have found this to be a useful reference text and would recommend it to those wishing to delve into the mathematical theory of basic queuing theory." (Michael NG, SIAM Review, Vol. 48 (3), 2006)

"The book under review attempts to give an introduction to the theory of queues without losing contact with its applicability. … For instructors who prefer the topics covered, this book is a nice candidate as they do not need to choose the topics but only need to elaborate on them. Nevertheless, it would be a good reference book for an introductory course in queuing theory, stochastic modelling, or applied probability, and a valuable one to add to a professional’s bookshelf." (N. Selvaraju, Mathematical Reviews, Issue 2007 c)

Authors and Affiliations

  • University of Trier, Germany

    L. Breuer, D. Baum

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