Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-12-03T19:20:05.015Z Has data issue: false hasContentIssue false
  • English
  • Français

SOJOURN TIMES IN THE M/G/1 FB QUEUE WITH LIGHT-TAILED SERVICE TIMES

Published online by Cambridge University Press:  22 June 2005

M. Mandjes  and
M. Nuyens
M. Mandjes
Affiliation:
CWI, Amsterdam, The Netherlands, and, KdV Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands, E-mail: [email protected]
M. Nuyens
Affiliation:
Department of Mathematics, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The asymptotic decay rate of the sojourn time of a customer in the stationary M/G/1 queue under the foreground–background (FB) service discipline is studied. The FB discipline gives service to those customers that have received the least service so far. We prove that for light-tailed service times, the decay rate of the sojourn time is equal to the decay rate of the busy period. It is shown that FB minimizes the decay rate in the class of work-conserving disciplines.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 3 , July 2005 , pp. 351 - 361
Copyright
© 2005 Cambridge University Press

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

REFERENCES

Borst, S., Boxma, O., Núñez Queija, R., & Zwart, A. (2003). The impact of the service discipline on delay asymptotics. Performance Evaluation 54: 175–206.Google Scholar
Cox, D. (1962). Renewal theory. London: Methuen.
Cox, D. & Smith, W. (1961). Queues. London: Methuen.
De Meyer, A. & Teugels, J. (1980). On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1. Journal of Applied Probability 17(3): 802–813.Google Scholar
Mandjes, M. & Zwart, A. Large deviations for waiting times in processor sharing queues (submitted).
Núñez Queija, R. (2000). Processor-sharing models for integrated-services networks. Ph.D. thesis, Eindhoven University, Eindhoven, The Netherlands.
Nuyens, M. (2004). The foreground–background queue. Ph.D. thesis, University of Amsterdam, Amsterdam.
Righter, R. (1994). Scheduling. In M. Shaked and J. Shanthikumar (eds.), Stochastic orders and their applications. San Diego, CA: Academic Press.
Righter, R. & Shanthikumar, J. (1989). Scheduling multiclass single server queueing systems to stochastically maximize the number of successful departures. Probability in the Engineering and Informational Sciences 3: 323–333.Google Scholar
Righter, R., Shanthikumar, J., & Yamazaki, G. (1990). On extremal service disciplines in single-stage queueing systems. Journal of Applied Probability 27: 409–416.Google Scholar