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On Regenerative Processes in Queueing Theory

  • Book
  • © 1976

Overview

Authors:
  1. J. W. Cohen

    1. Mathematical Institute, University of Utrecht, Utrecht, Netherlands

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 121)

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-IX
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  2. The single server queue GI/G/1

    • J. W. Cohen
    Pages 1-29

  3. The M/G/K system

    • J. W. Cohen
    Pages 31-70

  4. The M/G/1 system

    • J. W. Cohen
    Pages 71-90

  5. Back Matter

    Pages 91-96
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Keywords

About this book

I. The single server queue GIIG/1 1 1. 1 Definitions 1 1. 2 Regenerative processes 2 1. 3 The sequence n 1,2, . . . 4 = !::!n' 1. 4 The process t dO,co)} 11 {~t' The process t dO,co)} 1. 5 15 {~t' Applications to the GIIG/1 queue 1. 6 16 The average virtual waiting time during a busy 17 cycle ii. Little's formula 17 iii. The relation between the stationary distributions 18 of the virtual and actual waiting time iv. The relation between the distribution of the idle 20 period and the stationary distribution of the actual waiting time v. The limiting distribution of the residual service 24 time £. , -pw vi. The relation for ~ rn E{e -n} 25 n=O 1. 7 Some notes on chapter I 27 II. The M/G/K system 31 2. 1 On the stationary distribution of the actual and virtua131 waiting time for the M/G/K queueing system 2. 2 The M/G/K loss system 36 2. 3 Proof of Erlang's formula for the M/G/K loss system 43 i. Proof for the system MIMI'" 45 ii. Proof for the system M/G/co 47 VI iii. Proof fol' the MIG IK los s system III. The M/G/1 system 3. 1 Introduction 71 (K) 3. 2 Downcrossings of the ~t -process 74 3. 3 The distribution of the supremum of the virtual waiting 75 • (00) d' b 1 tlme ~t urlng a usy cyc e i. The exit probability 76 ii.

Authors and Affiliations

  • Mathematical Institute, University of Utrecht, Utrecht, Netherlands

    J. W. Cohen

Bibliographic Information

  • Book Title: On Regenerative Processes in Queueing Theory

  • Authors: J. W. Cohen

  • Series Title: Lecture Notes in Economics and Mathematical Systems

  • DOI: https://doi.org/10.1007/978-3-642-95281-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin · Heidelberg 1976

  • Softcover ISBN: 978-3-540-07627-8Published: 01 March 1976

  • eBook ISBN: 978-3-642-95281-4Published: 06 December 2012

  • Series ISSN: 0075-8442

  • Series E-ISSN: 2196-9957

  • Edition Number: 1

  • Number of Pages: IX, 93

  • Topics: Operations Research/Decision Theory

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