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On Regenerative Processes in Queueing Theory

  • J. W. Cohen

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

Table of contents

  1. Front Matter
    Pages I-IX
  2. J. W. Cohen
    Pages 1-29
  3. J. W. Cohen
    Pages 31-70
  4. J. W. Cohen
    Pages 71-90
  5. Back Matter
    Pages 91-96

About this book

Introduction

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.

Keywords

Distribution probability queueing theory service

Authors and affiliations

  • J. W. Cohen
    • 1
  1. 1.Mathematical InstituteUniversity of UtrechtUtrechtNetherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-95281-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1976
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-07627-8
  • Online ISBN 978-3-642-95281-4
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site