On Regenerative Processes in Queueing Theory

On Regenerative Processes in Queueing Theory by Jacob W. Cohen.

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 {{u0303}t' The process t dO,co)} 1. 5 15 {{u0303}t' Applications to the GIIG/1 queue 1. 6 16 The average virtual waiting time du...

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Bibliographic Details
Main Author: Cohen, Jacob W. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1976.
Edition:1st ed. 1976.
Series:Lecture Notes in Economics and Mathematical Systems, 121
Springer eBook Collection.
Subjects:
Operations research.
Decision making.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • I. The single server queue GI/G/1
  • 1.1 Definitions
  • 1.2 Regenerative processes
  • 1.3 The sequence wn, n = 1,2,…
  • 1.4 The process {v, t ?[0, ?)}
  • 1.5 The process {?t, t ?[0, ?)}
  • 1.6 Applications to the GI/G/1 queue
  • 1.7 Some notes on chapter I
  • II. The M/G/K system
  • 2.1 On the stationary distribution of the actual and virtual waiting time for the M/G/K queueing system
  • 2.2 The M/G/K loss system
  • 2.3 Proof of Erlang’s formula for the M/G/K loss system
  • III. The M/G/1 system
  • 3.1 Introduction
  • 3.2 Downcrossings of the vt(K) -process
  • 3.3 The distribution of the supremum of the virtual waiting time vt(?) during a busy cycle
  • 3.4 The distribution of the downcrossings 8l
  • 3.5 Derivation of the stationary distribution of the vt(K) - process, I
  • 3.6 Derivation of the stationary distribution of the vt(K) - process, II
  • 3.7 Some remarks on the actual and virtual waiting time processes
  • References.

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