Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article

Simple Near-Optimal Scheduling for the M/G/1

Published: 04 December 2019 Publication History

Abstract

We consider the problem of preemptively scheduling jobs to minimize mean response time of an M/G/1 queue. When the scheduler knows each job's size, the shortest remaining processing time (SRPT) policy is optimal. Unfortunately, in many settings we do not have access to each job's size. Instead, we know only the job size distribution. In this setting, the Gittins policy is known to minimize mean response time, but its complex priority structure can be computationally intractable. A much simpler alternative to Gittins is the shortest expected remaining processing time (SERPT) policy. While SERPT is a natural extension of SRPT to unknown job sizes, it is unknown how close SERPT is to optimal.

References

[1]
S. Aalto, U. Ayesta, and R. Righter. On the Gittins index in the M/G/1 queue. Queueing Systems, 63(1):437--458, 2009.
[2]
N. Bansal, B. Kamphorst, and B. Zwart. Achievable performance of blind policies in heavy traffic. Mathematics of Operations Research, 43(3):949--964, 2018.
[3]
L. Becchetti and S. Leonardi. Nonclairvoyant scheduling to minimize the total flow time on single and parallel machines. Journal of the ACM (JACM), 51(4):517--539, 2004.
[4]
H. Feng and V. Misra. Mixed scheduling disciplines for network flows. In ACM SIGMETRICS Performance Evaluation Review, volume 31, 36--39. ACM, 2003.
[5]
J. C. Gittins, K. D. Glazebrook, and R. Weber. Multi-armed Bandit Allocation Indices. John Wiley & Sons, 2011.
[6]
B. Kalyanasundaram and K. R. Pruhs. Minimizing flow time nonclairvoyantly. In Proceedings 38th Annual Symposium on Foundations of Computer Science, 345--352. IEEE, 1997.
[7]
B. Kamphorst and B. Zwart. Heavy-traffic analysis of sojourn time under the foreground-background scheduling policy. arXiv preprint arXiv:1712.03853, 2017.
[8]
R. Motwani, S. Phillips, and E. Torng. Nonclairvoyant scheduling. Theor. Comput. Sci., 130(1):17--47, 1994.
[9]
R. Righter and J. G. Shanthikumar. Scheduling multiclass single server queueing systems to stochastically maximize the number of successful departures. Probability in the Engineering and Informational Sciences, 3(3):323--333, 1989.
[10]
R. Righter, J. G. Shanthikumar, and G. Yamazaki. On extremal service disciplines in single-stage queueing systems. Journal of Applied Probability, 27(2):409--416, 1990.
[11]
L. Schrage. A proof of the optimality of the shortest remaining processing time discipline. Operations Research, 16(3):687-- 690, 1968.
[12]
Z. Scully, M. Harchol-Balter, and A. Scheller-Wolf. Soap: One clean analysis of all age-based scheduling policies. Proc. ACM Meas. Anal. Comput. Syst., 2(1):16:1--16:30, Apr. 2018.
[13]
Z. Scully, M. Harchol-Balter, and A. Scheller-Wolf. Simple near-optimal scheduling for the M/G/1. arXiv preprint arXiv:1907.10792, 2019.
[14]
A. Wierman, M. Harchol-Balter, and T. Osogami. Nearly insensitive bounds on SMART scheduling. In ACM SIGMETRICS Performance Evaluation Review, volume 33, 205--216. ACM, 2005.

Cited By

View all
  • (2024)Offline Learning-Based Multi-User Delay-Constrained Scheduling2024 IEEE 21st International Conference on Mobile Ad-Hoc and Smart Systems (MASS)10.1109/MASS62177.2024.00023(92-99)Online publication date: 23-Sep-2024
  • (2022)Effective multi-user delay-constrained scheduling with deep recurrent reinforcement learningProceedings of the Twenty-Third International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing10.1145/3492866.3549712(1-10)Online publication date: 3-Oct-2022

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM SIGMETRICS Performance Evaluation Review
ACM SIGMETRICS Performance Evaluation Review  Volume 47, Issue 2
September 2019
37 pages
ISSN:0163-5999
DOI:10.1145/3374888
Issue’s Table of Contents
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 04 December 2019
Published in SIGMETRICS Volume 47, Issue 2

Check for updates

Qualifiers

  • Research-article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)1
  • Downloads (Last 6 weeks)0
Reflects downloads up to 22 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2024)Offline Learning-Based Multi-User Delay-Constrained Scheduling2024 IEEE 21st International Conference on Mobile Ad-Hoc and Smart Systems (MASS)10.1109/MASS62177.2024.00023(92-99)Online publication date: 23-Sep-2024
  • (2022)Effective multi-user delay-constrained scheduling with deep recurrent reinforcement learningProceedings of the Twenty-Third International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing10.1145/3492866.3549712(1-10)Online publication date: 3-Oct-2022

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media