Table of contents

  1. Front Matter
    Pages i-xiii
  2. Muhammad El-Taha, Shaler Stidham Jr.
    Pages 1-33
  3. Muhammad El-Taha, Shaler Stidham Jr.
    Pages 35-50
  4. Muhammad El-Taha, Shaler Stidham Jr.
    Pages 51-80
  5. Muhammad El-Taha, Shaler Stidham Jr.
    Pages 81-115
  6. Muhammad El-Taha, Shaler Stidham Jr.
    Pages 117-157
  7. Muhammad El-Taha, Shaler Stidham Jr.
    Pages 159-212
  8. Muhammad El-Taha, Shaler Stidham Jr.
    Pages 213-233
  9. Muhammad El-Taha, Shaler Stidham Jr.
    Pages 235-247
  10. Back Matter
    Pages 249-295

About this book

Introduction

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.

Keywords

Ergodic theory Stochastic model Stochastic models Stochastic processes calculus point process queueing theory regenerative process stochastic process

Authors and affiliations

  • Muhammad El-Taha
    • 1
  • Shaler StidhamJr.
    • 2
  1. 1.University of Southern MaineUSA
  2. 2.University of North Carolina at Chapel HillUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-5721-0
  • Copyright Information Springer Science+Business Media New York 1999
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-7620-0
  • Online ISBN 978-1-4615-5721-0
  • Series Print ISSN 0884-8289
  • About this book