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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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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