Advertisement

Scheduling Multiple Flows on Parallel Disks

  • Ajay Gulati
  • Peter Varman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3769)

Abstract

We examine the problem of scheduling concurrent independent flows on multiple-disk I/O storage systems. Two models are considered: in the shared buffer model the memory buffer is shared among all the flows, while in the partitioned buffer model each flow has a private buffer. For the parallel disk model with d > 1 disks it is shown that the problem of minimizing the schedule length of n > 2 concurrent flows is NP-complete for both buffer models. A randomized scheduling algorithm for the partitioned buffer model is analyzed and probabilistic bounds on the schedule length are presented. Finally a heuristic based on static buffer allocation for the shared buffer model is discussed.

Keywords

Optimal Schedule Memory Buffer Schedule Length Multiple Flow Parallel Disk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gulati, A., Varman, P.: Lexicographic QoS scheduling for parallel I/O. In: Proceedings of the ACM Symposium on Parallelism in Algorithms and Architectures, Las Vegas, Nevada, United States, pp. 29–38. ACM Press, New York (2005)CrossRefGoogle Scholar
  2. 2.
    Albers, S., Garg, N., Leonardi, S.: Minimizing stall time in single and parallel disk systems. J. ACM 47, 969–986 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Cao, P., Felten, E.W., Karlin, A.R., Li, K.: A study of integrated prefetching and caching strategies. In: Proc. of the Joint Intl. Conf. on Measurement and Modeling of Computer Systems, pp. 188–197. ACM Press, New York (1995)Google Scholar
  4. 4.
    Kallahalla, M., Varman, P.J.: PC-OPT: optimal offline prefetching and caching for parallel I/O systems. IEEE Transactions on Computers 51, 1333–1344 (2002)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Kallahalla, M., Varman, P.: Optimal read-once parallel disk scheduling. In: Algorithmica (A preliminary version appeared in the 6th ACM IOPADS, 1999) (2005)Google Scholar
  6. 6.
    Hutchinson, D.A., Sanders, P., Vitter, J.S.: Duality between prefetching and queued writing with parallel disks. In: Proceedings of the 9th Annual European Symposium on Algorithms, Århus, Denmark, pp. 62–73. Springer, Heidelberg (2001)Google Scholar
  7. 7.
    Kimbrel, T., Karlin, A.R.: Near-optimal parallel prefetching and caching. SIAM J. Comput. 29, 1051–1082 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Patterson, R.H., Gibson, G., Ginting, E., Stodolsky, D., Zelenka, J.: Informed prefetching and caching. In: Proc. of the 15th ACM Symp. on Operating Systems Principles (1995)Google Scholar
  9. 9.
    Vitter, J.S., Shriver, E.A.M.: Optimal disk I/O with parallel block transfer. In: Proceedings of the twenty-second annual ACM symposium on Theory of computing. ACM Press, New York (1990)Google Scholar
  10. 10.
    Jin, W., Chase, J.S., Kaur, J.: Interposed proportional sharing for a storage service utility. SIGMETRICS Perform. Eval. Rev. 32, 37–48 (2004)CrossRefGoogle Scholar
  11. 11.
    Huang, L., Peng, G., Chiueh, T.C.: Multi-dimensional storage virtualization. SIGMETRICS Perform. Eval. Rev. 32, 14–24 (2004)CrossRefGoogle Scholar
  12. 12.
    Lumb, C., Merchant, A., Alvarez, G.: Façade: Virtual storage devices with performance guarantees. In: File and Storage technologies (FAST 2003), pp. 131–144 (2003)Google Scholar
  13. 13.
    Gulati, A.: Scheduling with QoS in parallel I/O systems. Master’s thesis, Rice University, Department of Computer Science (2004)Google Scholar
  14. 14.
    Gulati, A., Varman, P.: Scheduling with QoS in parallel I/O systems. In: International Workshop on Storage Network Architecture and Parallel I/Os (held in conjunction with PACT), Antibes Juan-les-pins, France (2004)Google Scholar
  15. 15.
    Leighton, F.T., Maggs, B.M., Rao, S.B.: Packet routing and job-shop scheduling in O(congestion + dilation) steps. In: Combinatorica, vol. 14, pp. 167–186 (1994)Google Scholar
  16. 16.
    Barve, R.D., Kallahalla, M., Varman, P.J., Vitter, J.S.: Competitive parallel disk prefetching and buffer management. Journal of Algorithms 36, 152–181 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Kallahalla, M., Varman, P.J.: Optimal prefetching and caching for parallel I/O systems. In: Proc. of 13th ACM Symp. on Parallel Algorithms and Architectures. ACM press, New York (2001)Google Scholar
  18. 18.
    Garey, M.R., Johnson, D.S.: Computers and intractability; a guide to the theory of NP-completeness. W. H. Freeman, New York (1979)zbMATHGoogle Scholar
  19. 19.
    Gonzalez, T., Sahni, S.: Flowship and jobshop schedules: Complexity and approximation. Operations research 26, 36–52 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Shmoys, D.B., Stein, C., Wein, J.: Improved approximation algorithms for shop scheduling problems. SIAM Journal on Computing 23, 617–632 (1994)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ajay Gulati
    • 1
  • Peter Varman
    • 2
  1. 1.Department of Computer Science 
  2. 2.Department of Electrical Engineering and Computer ScienceRice UniversityHoustonUSA

Personalised recommendations