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Intro Framework TEGs Computing Comparison Conclusion Computing the throughput of probabilistic and replicated streaming applications Anne Benoit, Fanny Dufoss e, Matthieu Gallet, Bruno Gaujal and Yves Robert Laboratoire de


  1. Intro Framework TEGs Computing Comparison Conclusion Computing the throughput of probabilistic and replicated streaming applications Anne Benoit, Fanny Dufoss´ e, Matthieu Gallet, Bruno Gaujal and Yves Robert Laboratoire de l’Informatique du Parall´ elisme ´ Ecole Normale Sup´ erieure de Lyon, France Roma Working Group Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 1/ 39

  2. Intro Framework TEGs Computing Comparison Conclusion Outline Introduction 1 Framework 2 Timed Event Graphs 3 Computing the throughput 4 Comparison results 5 Conclusion 6 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 2/ 39

  3. Intro Framework TEGs Computing Comparison Conclusion Outline Introduction 1 Framework 2 Timed Event Graphs 3 Computing the throughput 4 Comparison results 5 Conclusion 6 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 3/ 39

  4. Intro Framework TEGs Computing Comparison Conclusion Problem description We are given (i) a streaming application, dependence graph = linear chain; (ii) a one-to-many mapping of appliction onto heterogeneous platform; (iii) a set of I.I.D. (Independent and Identically-Distributed) variables to model computation/communication time in the mapping. How can we compute the throughput of the application, i.e., the rate at which data sets can be processed? Two execution models: Strict and Overlap Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 4/ 39

  5. Intro Framework TEGs Computing Comparison Conclusion Problem description We are given (i) a streaming application, dependence graph = linear chain; (ii) a one-to-many mapping of appliction onto heterogeneous platform; (iii) a set of I.I.D. (Independent and Identically-Distributed) variables to model computation/communication time in the mapping. How can we compute the throughput of the application, i.e., the rate at which data sets can be processed? Two execution models: Strict and Overlap Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 4/ 39

  6. Intro Framework TEGs Computing Comparison Conclusion Problem description We are given (i) a streaming application, dependence graph = linear chain; (ii) a one-to-many mapping of appliction onto heterogeneous platform; (iii) a set of I.I.D. (Independent and Identically-Distributed) variables to model computation/communication time in the mapping. How can we compute the throughput of the application, i.e., the rate at which data sets can be processed? Two execution models: Strict and Overlap Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 4/ 39

  7. Intro Framework TEGs Computing Comparison Conclusion Motivation No replication, i.e., one-to-one mapping: throughput dictated by critical hardware resource With replication, deterministic case: surprisingly difficult! (remember previous work, cases with no critical resources) Contributions: (i) general method (exponential cost) to compute throughput with I.I.E. exponential laws; (ii) bounds for arbitrary I.I.E. and N.B.U.E. (New Better than Used in Expectation) variables: between exponential and deterministic values; (iii) the problem of finding the optimal mapping is NP-complete. Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 5/ 39

  8. Intro Framework TEGs Computing Comparison Conclusion Motivation No replication, i.e., one-to-one mapping: throughput dictated by critical hardware resource With replication, deterministic case: surprisingly difficult! (remember previous work, cases with no critical resources) Contributions: (i) general method (exponential cost) to compute throughput with I.I.E. exponential laws; (ii) bounds for arbitrary I.I.E. and N.B.U.E. (New Better than Used in Expectation) variables: between exponential and deterministic values; (iii) the problem of finding the optimal mapping is NP-complete. Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 5/ 39

  9. Intro Framework TEGs Computing Comparison Conclusion Outline Introduction 1 Framework 2 Timed Event Graphs 3 Computing the throughput 4 Comparison results 5 Conclusion 6 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 6/ 39

  10. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  11. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  12. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  13. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  14. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  15. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  16. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  17. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  18. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  19. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  20. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  21. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  22. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  23. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  24. Intro Framework TEGs Computing Comparison Conclusion Application A linear workflow with many instances T 0 T 1 T 2 T 3 F 0 F 1 F 2 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 7/ 39

  25. Intro Framework TEGs Computing Comparison Conclusion Platform A fully connected platform Heterogeneous processors and communication links P 1 P 0 P 2 P 3 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 8/ 39

  26. Intro Framework TEGs Computing Comparison Conclusion Platform A fully connected platform Heterogeneous processors and communication links s 1 P 1 b 0 , 1 s 0 b 1 , 2 P 0 b 0 , 2 b 1 , 3 s 2 P 2 b 0 , 3 b 2 , 3 P 3 s 3 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 8/ 39

  27. Intro Framework TEGs Computing Comparison Conclusion Mapping A processor processes at most 1 task A task is mapped on possibly many processors Replication count of T i : R i Round-Robin distribution of each task T 0 T 1 T 2 T 3 F 0 F 1 F 2 R 2 = 3 R 0 = 1 R 1 = 2 R 3 = 1 P 3 P 1 P 0 P 4 P 6 P 2 P 5 Matthieu Gallet Roma Working Group, April 2010 Computing the throughput, probabilistic and replicated 9/ 39

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