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Sample-Path Analysis of Queueing Systems

  • Book
  • © 1999

Overview

Authors:
  1. Muhammad El-Taha

    1. University of Southern Maine, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Shaler Stidham

    1. University of North Carolina at Chapel Hill, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: International Series in Operations Research & Management Science (ISOR, volume 11)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction and Overview

    • Muhammad El-Taha, Shaler Stidham Jr.
    Pages 1-33

  3. Background and Fundamental Results

    • Muhammad El-Taha, Shaler Stidham Jr.
    Pages 35-50

  4. Processes with Imbedded Point Process: General State Space

    • Muhammad El-Taha, Shaler Stidham Jr.
    Pages 51-80

  5. Processes with Imbedded Point Process: Countable State Space

    • Muhammad El-Taha, Shaler Stidham Jr.
    Pages 81-115

  6. Sample-Path Stability

    • Muhammad El-Taha, Shaler Stidham Jr.
    Pages 117-157

  7. Little’s Formula and Extensions

    • Muhammad El-Taha, Shaler Stidham Jr.
    Pages 159-212

  8. Insensitivity of Queueing Networks

    • Muhammad El-Taha, Shaler Stidham Jr.
    Pages 213-233

  9. Sample-Path Approach to Palm Calculus

    • Muhammad El-Taha, Shaler Stidham Jr.
    Pages 235-247

  10. Back Matter

    Pages 249-295
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Keywords

About this book

Sample-Path Analysis of Queueing Systems uses a deterministic (sample-path) approach to analyze stochastic systems, primarily queueing systems and more general input-output systems. Among other topics of interest it deals with establishing fundamental relations between asymptotic frequencies and averages, pathwise stability, and insensitivity. These results are utilized to establish useful performance measures. The intuitive deterministic approach of this book will give researchers, teachers, practitioners, and students better insights into many results in queueing theory. The simplicity and intuitive appeal of the arguments will make these results more accessible, with no sacrifice of mathematical rigor. Recent topics such as pathwise stability are also covered in this context.
The book consistently takes the point of view of focusing on one sample path of a stochastic process. Hence, it is devoted to providing pure sample-path arguments. With this approach it is possible to separate the issue of the validity of a relationship from issues of existence of limits and/or construction of stationary framework. Generally, in many cases of interest in queueing theory, relations hold, assuming limits exist, and the proofs are elementary and intuitive. In other cases, proofs of the existence of limits will require the heavy machinery of stochastic processes. The authors feel that sample-path analysis can be best used to provide general results that are independent of stochastic assumptions, complemented by use of probabilistic arguments to carry out a more detailed analysis. This book focuses on the first part of the picture. It does however, provide numerous examples that invoke stochastic assumptions, which typically are presented at the ends of the chapters.

Reviews

` ... it contains a wealth of useful material for those giving courses in stochastic processes at all levels, and its extremely readable style makes it suitable for anyone with previous exposure to basic probability and stochastic processes.'
Short Book Reviews, 19:2 (1999)
`... this monograph is well written, fairly comprehensive and a welcome addition to the growing number of books on queuing theory. It is of interest to a wide audience of operations researchers, applied probabilists and engineers.'
Mathematical reviews, 2002d

Authors and Affiliations

  • University of Southern Maine, USA

    Muhammad El-Taha

  • University of North Carolina at Chapel Hill, USA

    Shaler Stidham

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