Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • The covariance function of the virtual waiting-time process in an M/G/1 queue

  • Teunis J. Ott
  • Journal:
    Advances in Applied Probability / Volume 9 / Issue 1 / March 1977
    Published online by Cambridge University Press:
    01 July 2016, pp. 158-168
    Print publication:
    March 1977

  • Let R(t) be the covariance function of the stationary virtual waiting-time process of a stable M/G/1 queue. It is proven that if R(t) exists, i.e., if the service-times have a finite third moment, then R(t) is positive and convex on [0, ∞), with an absolutely continuous derivative R’ and a bounded, non-negative second derivative R″. Also, and R″ cannot be chosen monotone. Contrary to a finding by Beneš [1] it is proven that if and only if the service-times have a finite fourth moment.

  • The stable M/G/1 queue in heavy traffic and its covariance function

  • Teunis J. Ott
  • Journal:
    Advances in Applied Probability / Volume 9 / Issue 1 / March 1977
    Published online by Cambridge University Press:
    01 July 2016, pp. 169-186
    Print publication:
    March 1977

  • Let X(t) be the virtual waiting-time process of a stable M/G/1 queue. Let R(t) be the covariance function of the stationary process X(t), B(t) the busy-period distribution of X(t); and let E(t) = P{X(t) = 0|X(0) = 0}.

    For X(t) some heavy-traffic results are given, among which are limiting expressions for R(t) and its derivatives and for B(t) and E(t).

    These results are used to find the covariance function of stationary Brownian motion on [0, ∞).