Unfairness Metrics for Space-Sharing Parallel Job Schedulers

  • Gerald Sabin
  • P. Sadayappan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3834)

Abstract

Sociology, computer networking and operations research provide evidence of the importance of fairness in queuing disciplines. Currently, there is no accepted model for characterizing fairness in parallel job scheduling. We introduce two fairness metrics intended for parallel job schedulers, both of which are based on models from sociology, networking, and operations research. The first metric is motivated by social justice and attempts to measure deviation from arrival order, which is perceived as fair by the end user. The second metric is based on resource equality and compares the resources consumed by a job with the resources deserved by the job. Both of these metrics are orthogonal to traditional metrics, such as turnaround time and utilization.

The proposed fairness metrics are used to measure the unfairness for some typical scheduling policies via simulation studies. We analyze the fairness of these scheduling policies using both metrics, identifying similarities and differences.

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References

  1. 1.
    Talby, D., Feitelson, D.: Supporting priorities and improving utilization of the IBM SP scheduler using slack-based backfilling. In: Proceedings of the 13th International Parallel Processing Symposium (1999)Google Scholar
  2. 2.
    Mu’alem, A., Feitelson, D.: Utilization, predictability, workloads, and user runtime estimates in scheduling the IBM SP2 with backfilling. IEEE Transactions on Parallel and Distributed Systems 12, 529–543 (2001)CrossRefGoogle Scholar
  3. 3.
    Sabin, G., Kettimuthu, R., Rajan, A., Sadayappan, P.: Scheduling of parallel jobs in a heterogeneous multi-site environement. In: Feitelson, D.G., Rudolph, L., Schwiegelshohn, U. (eds.) JSSPP 2003. LNCS, vol. 2862, pp. 87–104. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Islam, M., Balaji, P., Sadayappan, P., Panda, D.K.: QoPS: A QoS based scheme for parallel job scheduling. In: Feitelson, D.G., Rudolph, L., Schwiegelshohn, U. (eds.) JSSPP 2003. LNCS, vol. 2862, pp. 252–268. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Feitelson, D.: Workshops on job scheduling strategies for parallel processing, http://www.cs.huji.ac.il/~feit/parsched/
  6. 6.
    Shmueli, E., Feitelson, D.: Backfilling with lookahead to optimize the performance of parallel job scheduling. In: Feitelson, D.G., Rudolph, L., Schwiegelshohn, U. (eds.) JSSPP 2003. LNCS, vol. 2862, pp. 228–251. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Srinivasan, S., Kettimuthu, R., Subramani, V., Sadayappan, P.: Characterization of backfilling strategies for job scheduling. In: 2002 Intl. Workshops on Parallel Processing (2002); held in conjunction with the 2002 Intl. Conf. on Parallel Processing, ICPP 2002Google Scholar
  8. 8.
    Raz, D., Levy, H., Avi-Itzhak, B.: A resource-allocation queueing fairness measure. In: Proceedings of Sigmetrics 2004/Performance 2004 Joint Conference on Measurement and Modeling of Computer Systems, New York, NY, pp. 130–141 (2004); Also appears as Performance Evaluation Review Special Issue 32(1), 130–141Google Scholar
  9. 9.
    Avi-Itzhak, B., Levy, H., Raz, D.: Quantifying fairness in queueing systems: Principles and applications. Technical Report RRR-26-2004, RUTCOR, Rutgers University (2004)Google Scholar
  10. 10.
    Raz, D., Levy, H., Avi-Itzhak, B.: RAQFM: a resource allocation queueing fairness measure. Technical Report RRR-32-2004, RUTCOR, Rutgers University (2004)Google Scholar
  11. 11.
    Mann, L.: Queue culture: The waiting line as a social system. The American Journal of Sociology 75, 340–354 (1969)CrossRefGoogle Scholar
  12. 12.
    Larson, R.: Perspectives on queues: Social justice and the psychology of queueing. Operations Research 35, 895–905 (1987)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Gordon, E.S.: Slips and Skips in Queues. PhD thesis, Massachusetts Institute of Technology (1989)Google Scholar
  14. 14.
    Whitt, W.: The amount of overtaking in a network of queues. Networks 14, 411–426 (1984)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Rafaeli, A., Kedmi, E., Vashdi, D., Barron, G.: Queues and fairness: A multiple study experimental investigation, http://queues-fairness.rafaeli.net/
  16. 16.
    Greenberg, A.G., Madras, N.: How fair is fair queueing? Association for Computing Machinery 39, 568–598 (1992)MATHMathSciNetGoogle Scholar
  17. 17.
    Demers, A., Keshav, S., Shenker, S.: Analysis and simulation of a fair queueing algorithm. Internetworking Research and Experience 1, 3–26 (1990)Google Scholar
  18. 18.
    Nandagopal, T., Lu, S., Bharghavan, V.: A unified architecture for the design and evaluation of wireless fair queueing algorithms. Wireless Networks 8, 231–247 (2002)MATHCrossRefGoogle Scholar
  19. 19.
    Wierman, A., Harchol-Balter, M.: Classifying scheduling policies with respect to unfairness in an M/GI/1. In: Proceedings of the 2003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems, pp. 238–249 (2003)Google Scholar
  20. 20.
    Bansal, N., Harcol-Balter, M.: Analysis of SRPT scheduling: Investigating unfairness. In: SIGMETRICS (2001)Google Scholar
  21. 21.
    Harchol-Balter, M., Sigman, K., Wierman, A.: Asymptotic convergence of scheduling policies with respect to slowdown. In: IFIP WG 7.3 International Symposium on Computer Modeling, Measurement and Evaluation (2002)Google Scholar
  22. 22.
    Schwiegelshohn, U., Yahyapour, R.: Fairness in parallel job scheduling. Journal of Scheduling 5, 297–320 (2000)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Sabin, G., Sahasrabudhe, V., Sadayappan, P.: On fairness in distributed job scheduling across multiple sites. In: Cluster (2004)Google Scholar
  24. 24.
    Sabin, G., Kochhar, G., Sadayappan, P.: Job fairness in non-preemptive job scheduling. In: International Conference on Parallel Processesing (2004)Google Scholar
  25. 25.
    Feitelson, D.G.: Logs of real parallel workloads from production systems, http://www.cs.huji.ac.il/labs/parallel/workload/
  26. 26.
    Hansen, B.: An analysis of response ratio. In: IFIP Congress (1971)Google Scholar
  27. 27.
    Weisstein, E.W.: Spearman rank correlation coefficient, http://mathworld.wolfram.com/SpearmanRankCorrelationCoefficient.html From MathWorld–A Wolfram Web Resource

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Gerald Sabin
    • 1
  • P. Sadayappan
    • 1
  1. 1.The Ohio State UniversityColumbusUSA

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