Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T04:45:49.968Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Markov property of the GI/G/∞ Gaussian limit

Published online by Cambridge University Press:  01 July 2016

Peter W. Glynn
Peter W. Glynn*
Affiliation:
Stanford University
*
∗Postal address: Department of Operations Research, Stanford University, Stanford, CA 94305, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that the heavy-traffic Gaussian limit for GI/G/∞ queues is Markovian if and only if the service-time distribution H(t) is of the form 1-H(t) = pe–αt for α > 0 and 0 < p ≦ 1.

Keywords

GI/G/s QUEUELIMIT THEOREM: GAUSSIAN PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 1 , March 1982 , pp. 191 - 194
Copyright
Copyright © Applied Probability Trust 1982 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research was supported under National Science Foundation Grant MCS 79-09139, Office of Naval Research Contract N00014-76-C-0578 (NR 042-343), and a Natural Sciences and Engineering Research Council of Canada Postgraduate Scholarship.

References

Borovkov, A. A. (1967) On limit laws for service processes in multi-channel systems. Siberian Math. J. 8, 746–763.Google Scholar
Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
Feller, W. (1950) An Introduction to Probability Theory and its Applications, Vol. 1. Wiley, New York.Google Scholar
Iglehart, D. L. (1965) Limit diffusion approximations for the many server queue and the repairman problem. J. Appl. Prob. 2, 429–441.Google Scholar
Whitt, W. (1981) On the heavy-traffic limit theorem for GI/G/∞ queues. Adv. Appl. Prob. 14, 171–190.Google Scholar