Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T14:12:28.691Z Has data issue: false hasContentIssue false
  • English
  • Français

On the nonoptimality of the foreground-background discipline for IMRL service times

Part of: Special processes Operations research and management science Computer system organization

Published online by Cambridge University Press:  14 July 2016

S. Aalto  and
U. Ayesta
S. Aalto*
Affiliation:
Helsinki University of Technology
U. Ayesta
Affiliation:
CWI
*
∗Postal address: Networking Laboratory, Helsinki University of Technology, PO Box 3000, FIN-02015 HUT, Finland. Email address: samuli.aalto@tkk.fi
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is known that for decreasing hazard rate (DHR) service times the foreground-background discipline (FB) minimizes the mean delay in the M/G/1 queue among all work-conserving and nonanticipating service disciplines. It is believed that a similar result is valid for increasing mean residual lifetime (IMRL) service times. However, on the one hand, we point out a flaw in an earlier proof of the latter result and construct a counter-example that demonstrates that FB is not necessarily optimal within class IMRL. On the other hand, we prove that the mean delay for FB is smaller than that of the processor-sharing discipline within class IMRL, giving a weaker version of an earlier hypothesis.

Keywords

Queueing theoryschedulingM/G/1IMRLmean delayFBPSMLPS

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M20: Performance evaluation; queueing; scheduling 90B22: Queues and service 90B36: Scheduling theory, stochastic
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 2 , June 2006 , pp. 523 - 534
Copyright
© Applied Probability Trust 2006 

Footnotes

∗∗

Current address: LAAS-CNRS, 7 Avenue de Colonel Roche, 31 077 Toulouse Cedex 4, France. Email address: urtzi.ayesta@laas.fr

References

Aalto, S., Ayesta, U. and Nyberg-Oksanen, E. (2004). Two-level processor-sharing scheduling disciplines: mean delay analysis. In ACM SIGMETRICS Performance Evaluation Review (Proc. SIGMETRICS 2004/PERFORMANCE 2004), Association for Computing Machinery, New York, pp. 97–105.Google Scholar
Coffman, E. G. Jr. and Denning, P. J. (1973). Operating Systems Theory. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Kleinrock, L. (1976). Queueing Systems, Vol. II, Computer Applications. John Wiley, New York.Google Scholar
Righter, R. and Shanthikumar, J. G. (1989). Scheduling multiclass single server queueing systems to stochastically maximize the number of successful departures. Prob. Eng. Inf. Sci. 3, 323–333.Google Scholar
Righter, R., Shanthikumar, J. G. and Yamazaki, G. (1990). On extremal service disciplines in single-stage queueing systems. J. Appl. Prob. 27, 409–416.Google Scholar
Wierman, A., Bansal, N. and Harchol-Balter, M. (2004). A note on comparing response times in the M/GI/1/FB and M/GI/1/PS queues. Operat. Res. Lett. 32, 73–76.Google Scholar
Yashkov, S. F. (1987). Processor-sharing queues: some progress in analysis. Queueing Systems 2, 1–17.CrossRefGoogle Scholar