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Mathematical Methods in Queuing Theory

  • Book
  • © 1994

Overview

Authors:
  1. Vladimir V. Kalashnikov

    1. Institute for System Studies, Moscow, Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 271)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-4
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  2. Queueing Theory

    • Vladimir V. Kalashnikov
    Pages 5-15

  3. Necessary Facts from Probability Theory and the Theory of Analytic Functions

    • Vladimir V. Kalashnikov
    Pages 16-53

  4. Random Flows

    • Vladimir V. Kalashnikov
    Pages 54-79

  5. Elementary Methods in Queueing Theory

    • Vladimir V. Kalashnikov
    Pages 80-102

  6. Markov Chains

    • Vladimir V. Kalashnikov
    Pages 103-162

  7. Renewal Processes

    • Vladimir V. Kalashnikov
    Pages 163-200

  8. Regenerative Processes

    • Vladimir V. Kalashnikov
    Pages 201-232

  9. Discrete-Time Markov Queueing Models

    • Vladimir V. Kalashnikov
    Pages 233-260

  10. Markov Queueing Models

    • Vladimir V. Kalashnikov
    Pages 261-295

  11. Method of Supplementary Variables

    • Vladimir V. Kalashnikov
    Pages 296-321

  12. First-Occurrence Events

    • Vladimir V. Kalashnikov
    Pages 322-363

  13. Back Matter

    Pages 364-381
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Keywords

About this book

The material of this book is based on several courses which have been delivered for a long time at the Moscow Institute for Physics and Technology. Some parts have formed the subject of lectures given at various universities throughout the world: Freie Universitat of Berlin, Chalmers University of Technology and the University of Goteborg, University of California at Santa Barbara and others. The subject of the book is the theory of queues. This theory, as a mathematical discipline, begins with the work of A. Erlang, who examined a model of a telephone station and obtained the famous formula for the distribution of the number of busy lines which is named after him. Queueing theory has been applied to the study of numerous models: emergency aid, road traffic, computer systems, etc. Besides, it has lead to several related disciplines such as reliability and inventory theories which deal with similar models. Nevertheless, many parts of the theory of queues were developed as a "pure science" with no practical applications. The aim of this book is to give the reader an insight into the mathematical methods which can be used in queueing theory and to present examples of solving problems with the help of these methods. Of course, the choice of the methods is quite subjective. Thus, many prominent results have not even been mentioned.

Authors and Affiliations

  • Institute for System Studies, Moscow, Russia

    Vladimir V. Kalashnikov

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