Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T23:26:02.284Z Has data issue: false hasContentIssue false
  • English
  • Français

On two stationary distributions for the stable GI/G/1 queue

Published online by Cambridge University Press:  14 July 2016

Austin J. Lemoine
Austin J. Lemoine*
Affiliation:
Clemson University, South Carolina
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper provides simple proofs of two standard results for the stable GI/G/1 queue on the structure of the distribution functions of the stationary virtual waiting time and the stationary queue-length Our argument is applicable to more general single server systems than the queue GI/G/1.

Keywords

STABLE G//G/1 QUEUESTATIONARY VIRTUAL WAITING TIMESTATIONARY QUEUE-LENGTHSTATIONARY ACTUAL WAITING TIME
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 849 - 852
Copyright
Copyright © Applied Probability Trust 1974 

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

Research supported by N.S.F. Grant No. GK-39073.

References

[1]Cohen, J. W. (1969) The Single Server Queue. North Holland, Amsterdam.Google Scholar
[2]Lemoine, A. J. (1974) Limit theorems for generalized single server queues. Adv. Appl. Prob. 6, 159–174.Google Scholar
[3]Lemoine, A. J. (1974) Limit theorems for generalized single server queues: the exceptional system. SIAM J. Appl. Math. To appear.Google Scholar
[4]Takács, L. (1963) The limiting distribution of the virtual waiting time and the queue size for a single-server queue with recurrent input and general service times. Sankyha A 25, 91–100.Google Scholar