Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-12-01T06:53:32.844Z Has data issue: false hasContentIssue false
  • English
  • Français

On remaining full busy periods of GI/G/c queues and their relation to stationary point processes

Published online by Cambridge University Press:  14 July 2016

Saeed Ghahramani
Saeed Ghahramani*
Affiliation:
Towson State University
*
∗Postal address: Towson State University, Department of Mathematics, Towson, MD 21204, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

For a GI/G/c queue, a full busy period is a period commencing when an arrival finds c − 1 customers in the system and ending when, for the first time after that, a departure leaves behind c − 1 customers in the system. We show that given a full busy period is found to be in progress at a random epoch, the remaining full busy period has the equilibrium distribution. Moreover, we demonstrate that this property is typical for a broad class of stationary random processes.

Keywords

FULL AND PARTIAL BUSY PERIODSREMAINING BUSY PERIODS
Type
Short Communications
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 232 - 236
Copyright
Copyright © Applied Probability Trust 1990 

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.)

References

[1] Asmussen, S. (1987) Applied Probability and Queues. Wiley, New York.Google Scholar
[2] Brown, M. and Ross, S. M. (1972) Asymptotic properties of cumulative processes. SIAM J. Appl. Math. 22, 93–105.CrossRefGoogle Scholar
[3] Kiefer, J. and Wolfowitz, J. (1956) On the characteristics of the general queuing process with applications to random walks. Ann. Math. Statist. 27, 147–161.Google Scholar
[4] Rolski, T. (1981) Stationary Random Processes Associated with Point Processes. Lecture Notes in Statistics 5, Springer-Verlag, Berlin.CrossRefGoogle Scholar
[5] Whitt, W. (1972) Embedded renewal processes in the GI/G/s queue. J. Appl. Prob. 9, 650–658.Google Scholar