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Classifying scheduling policies with respect to higher moments of conditional response time

Published: 06 June 2005 Publication History

Abstract

In addition to providing small mean response times, modern applications seek to provide users predictable service and, in some cases, Quality of Service (QoS) guarantees. In order to understand the predictability of response times under a range of scheduling policies, we study the conditional variance in response times seen by jobs of different sizes. We define a metric and a criterion that distinguish between contrasting functional behaviors of conditional variance, and we then classify large groups of scheduling policies.In addition to studying the conditional variance of response times, we also derive metrics appropriate for comparing higher conditional moments of response time across job sizes. We illustrate that common statistics such as raw and central moments are not appropriate when comparing higher conditional moments of response time. Instead, we find that cumulant moments should be used.

References

[1]
N. Bansal and M. Harchol-Balter. Analysis of SRPT scheduling: Investigating unfairness. In Proceedings of ACM Sigmetrics, 2001.]]
[2]
M. Bender, S. Chakrabarti, and S. Muthukrishnan. Flow and stretch metrics for scheduling continous job streams. In Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, 1998.]]
[3]
B. Dellart. How tolerable is delay? consumers evaluations of internet web sites after waiting. J. of Interactive Marketing, 13:41--54, 1999.]]
[4]
N. Duffield, W. Massey, and W. Whitt. A nonstationary offered-load model for packet networks. Telecommunication Systems, 13:271--296, 2001.]]
[5]
E. Friedman and S. Henderson. Fairness and efficiency in web server protocols. In Proceedings of ACM Sigmetrics, 2003.]]
[6]
G. L. Choudhury and W. Whitt. Heavy-traffic asymptotic expansions for the asymptotic decay rates in the BMAP/G/1 queue. Stochastic Models, 10:453--498, 1994.]]
[7]
M. Gong and C. Williamson. Quantifying the properties of SRPT scheduling. In IEEE/ACM Symposium on Mod., Anal., and Sim. of Comp. and Telecomm. Sys. (MASCOTS), 2003.]]
[8]
I. Gradshteyn and I. Ryzhik. Tables of Integrals, Series, and Products. Academic Press, 2000.]]
[9]
M. Harchol-Balter, B. Schroeder, N. Bansal, and M. Agrawal. Implementation of SRPT scheduling in web servers. ACM Transactions on Computer Systems, 21(2), May 2003.]]
[10]
M. Harchol-Balter, K. Sigman, and A. Wierman. Asymptotic convergence of scheduling policies with respect to slowdown. Performance Evaluation, 49(1-4):241--256, 2002.]]
[11]
M. Kendall. The Advanced Theory of Statistics. Griffin, London, 1945.]]
[12]
L. Kleinrock. Queueing Systems, volume I. Theory. John Wiley & Sons, 1975.]]
[13]
L. Kleinrock. Queueing Systems, volume II. Computer Applications. John Wiley & Sons, 1976.]]
[14]
T. Matis and R. Feldman. Using cumulant functions in queueing theory. Queueing Systems, 40:341--353, 2002.]]
[15]
R. Nunez-Queija. Queues with equally heavy sojourn time and service requirement distributions. Ann. Oper. Res, 113:101--117, 2002.]]
[16]
T. Osogami and M. Harchol-Balter. A closed-form solution for mapping general distributions to minimal PH distributions. In Modelling Tools and Techniques for Comp. and Comm. System Perf. Eval., 2003.]]
[17]
I. Rai, G. Urvoy-Keller, and E. Biersack. Analysis of LAS scheduling for job size distributions with high variance. In Proceedings of ACM Sigmetrics, 2003.]]
[18]
I. A. Rai, G. Urvoy-Keller, M. Vernon, and E. W. Biersack. Performance modeling of LAS based scheduling in packet switched networks. In Proc. of ACM Sigmetrics-Performance, 2004.]]
[19]
M. Rawat and A. Kshemkalyani. SWIFT: Scheduling in web servers for fast response time. In Symp. on Network Computing and App., 2003.]]
[20]
D. Raz, H. Levy, and B. Avi-Itzhak. A resource-allocation queueing fairness measure. In Proc. of ACM Sigmetrics-Performance, 2004.]]
[21]
R. Righter, J. Shanthikumar, and G. Yamazaki. On external service disciplines in single stage queueing systems. J. of Applied Probability, 27:409--416, 1990.]]
[22]
S. Ross. Introduction to Probability Models. Academic Press, 1997.]]
[23]
L. E. Schrage. A proof of the optimality of the shortest remaining processing time discipline. Operations Research, 16:678--690, 1968.]]
[24]
L. E. Schrage and L. W. Miller. The queue M/G/1 with the shortest remaining processing time discipline. Operations Research, 14:670--684, 1966.]]
[25]
A. Silberschatz and P. Galvin. Operating System Concepts, 5th Edition. John Wiley & Sons, 1998.]]
[26]
H. Takagi. Queueing Analysis: Volume 1: Vacation and Priority Systems. North-Holland, 1991.]]
[27]
A. Tanenbaum. Modern Operating Systems. Prentice Hall, 1992.]]
[28]
A. Ward and W. Whitt. Predicting response times in processor-sharing queues. In Proc. of the Fields Institute Conf. on Comm. Networks, 2000.]]
[29]
W. Whitt. Improving service by informing jobs about anticipated delays. Managemet Science, 45:870--888, 1999.]]
[30]
W. Whitt. Predicting queueing delays. Management Science, 45:192--207, 1999.]]
[31]
A. Wierman and M. Harchol-Balter. Classifying scheduling policies with respect to unfairness in an M/GI/1. In Proceedings of ACM Sigmetrics, 2003.]]
[32]
A. Wierman, M. Harchol-Balter, and T. Osogami. Nearly insensitive bounds on SMART scheduling. In Proc. of ACM Sigmetrics, 2005.]]
[33]
S. Yang and G. de Veciana. Enhancing both network and user performance for networks supporting best effort traffic. volume 12, pages 349--360, 2004.]]
[34]
S. Yashkov. Processor sharing queues: Some progress in analysis. Queueing Systems, 2:1--17, 1987.]]
[35]
S. Yashkov. Mathematical problems in the theory of shared-processor systems. J. of Soviet Mathematics, 58:101--147, 1992.]]
[36]
M. Zhou and L. Zhou. How does waiting duration information influence customers' reactions to waiting for services. J. of Applied Social Psychology, 26:1702--1717, 1996.]]
[37]
A. Zwart and O. Boxma. Sojourn time asymptotics in the M/G/1 processor sharing queue. Queueing Sys. Thry. and App., 35:141--166, 2000.]]

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Published In

cover image ACM SIGMETRICS Performance Evaluation Review
ACM SIGMETRICS Performance Evaluation Review  Volume 33, Issue 1
Performance evaluation review
June 2005
417 pages
ISSN:0163-5999
DOI:10.1145/1071690
Issue’s Table of Contents
  • cover image ACM Conferences
    SIGMETRICS '05: Proceedings of the 2005 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
    June 2005
    428 pages
    ISBN:1595930221
    DOI:10.1145/1064212
Permission to make digital or hard copies of all or part 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 components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 06 June 2005
Published in SIGMETRICS Volume 33, Issue 1

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Author Tags

  1. FB
  2. LAS
  3. M/G/1
  4. PS
  5. PSJF
  6. SET
  7. SRPT
  8. cumulants
  9. foreground-background
  10. least attained service
  11. predictability
  12. processor sharing
  13. response time
  14. scheduling
  15. shortest job first
  16. shortest remaining processing time
  17. variance

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