Advertisement

Throughput analysis of dataflow graphs

  • Robert de Groote
Chapter

Abstract

Static dataflow graphs such as those presented in earlier chapters are attractive from a performance point of view, as the rate at which data is processed can be assessed beforehand. Assessing this performance involves analysing the dependency structure and the timings of the different nodes. This chapter describes different ways to approach this problem, and provides a mathematical basis from which these approaches follow. Methods for efficiently analysing the throughput are given, for single-rate (or homogeneous) graphs, synchronous dataflow graphs, and cyclo-static dataflow graphs.

References

  1. 1.
    Mohamed Bamakhrama and Todor Stefanov. Hard-real-time scheduling of data-dependent tasks in embedded streaming applications. In Proceedings of the ninth ACM international conference on Embedded software, pages 195–204. ACM, 2011.Google Scholar
  2. 2.
    Mohamed Bamakhrama and Todor Stefanov. On the hard-real-time scheduling of embedded streaming applications. Design Automation for Embedded Systems, 17(2):221–249, 2013.CrossRefGoogle Scholar
  3. 3.
    Richard Bellman. On a routing problem. Quarterly of applied mathematics, 16(1):87–90, 1958.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Mohamed Benazouz, Olivier Marchetti, Alix Munier-Kordon, and Thierry Michel. A new method for minimizing buffer sizes for Cyclo-Static Dataflow graphs. In 8th IEEE Workshop on Embedded Systems for Real-Time Multimedia, pages 11–20. IEEE, Oct 2010.Google Scholar
  5. 5.
    Mohamed Benazouz, Alix Munier-Kordon, Thomas Hujsa, and Bruno Bodin. Liveness evaluation of a cyclo-static DataFlow graph. In Proceedings of the 50th Annual Design Automation Conference on - DAC ’13, page 1, New York, New York, USA, May 2013. ACM Press.Google Scholar
  6. 6.
    G. Bilsen, M. Engels, R. Lauwereins, and J. Peperstraete. Cyclo-Static dataflow. IEEE Transactions on Signal Processing, 44(2):397–408, 1996.CrossRefGoogle Scholar
  7. 7.
    B. Bodin, A. Munier-Kordon, and B.D. de Dinechin. K-periodic schedules for evaluating the maximum throughput of a synchronous dataflow graph. In Proceedings of the International Conference on Embedded Computer Systems (SAMOS), pages 152–159, July 2012.Google Scholar
  8. 8.
    Bruno Bodin, Alix Munier-Kordon, and Benoit Dupont de Dinechin. Periodic schedules for Cyclo-Static Dataflow. In Proceedings of the 11th IEEE Symposium on Embedded Systems for Real-time Multimedia, pages 105–114. IEEE, October 2013.Google Scholar
  9. 9.
    Bruno Bodin, Alix Munier-Kordon, and Benoît Dupont de Dinechin. Optimal and fast throughput evaluation of csdf. In Proceedings of the 53rd Annual Design Automation Conference, page 160. ACM, 2016.Google Scholar
  10. 10.
    Jean Cochet-terrasson, Guy Cohen, Stéphane Gaubert, Michael Mc Gettrick, and Jean-Pierre Quadrat. Numerical Computation of Spectral Elements in Max-Plus Algebra. In Proceedings of the IFAC Conference on System Structure and Control, July 1998.Google Scholar
  11. 11.
    G. Cohen, S. Gaubert, and Jean-Pierre Quadrat. Timed-event graphs with multipliers and homogeneous min-plus systems. IEEE Transactions on Automatic Control, 43(9):1296–1302, 1998.MathSciNetCrossRefGoogle Scholar
  12. 12.
    Guy Cohen, Geert Jan Olsder, and Jean-Pierre Quadrat. Synchronization and linearity: an algebra for discrete event systems. Wiley New York, 1992.Google Scholar
  13. 13.
    Ali Dasdan. Experimental analysis of the fastest optimum cycle ratio and mean algorithms. ACM Transactions on Design Automation of Electronic Systems (TODAES), 9(4):385–418, 2004.CrossRefGoogle Scholar
  14. 14.
    Robert de Groote. On the Analysis of Synchronous Dataflow Graphs: a System-theoretic Perspective. PhD thesis, University of Twente, the Netherlands, February 2016.Google Scholar
  15. 15.
    Robert de Groote, Philip K. F. Hölzenspies, Jan Kuper, and Gerard J. M. Smit. Multi-rate Equivalents of Cyclo-Static Synchronous Dataflow Graphs. In Proceedings of the 14th International Conference on Application of Concurrency to System Design (ACSD), pages 62–71. IEEE Computer Society, June 2014.Google Scholar
  16. 16.
    Robert de Groote, Philip K. F. Hölzenspies, Jan Kuper, and Gerard J. M. Smit. Single-Rate Approximations of Cyclo-Static Synchronous Dataflow Graphs. In Proceedings of the 17th International Workshop on Software and Compilers for Embedded Systems (SCOPES), pages 11–20, June 2014.Google Scholar
  17. 17.
    Robert de Groote, Jan Kuper, Hajo Broersma, and Gerard J.M. Smit. Max-Plus Algebraic Throughput Analysis of Synchronous Dataflow Graphs. In Proceedings of the 38th Euromicro Conference on Software Engineering and Advanced Applications (SEAA), pages 29–38. IEEE, September 2012.Google Scholar
  18. 18.
    M. Engels, G. Bilsen, R. Lauwereins, and J. Peperstraete. Cycle-static dataflow: model and implementation. In Proceedings of the 28th Asilomar Conference on Signals, Systems and Computers, volume 1, pages 503–507. IEEE Comput. Soc. Press, 1994.Google Scholar
  19. 19.
    Marc Geilen. Synchronous dataflow scenarios. ACM Transactions on Embedded Computing Systems, 10(2):1–31, December 2010.MathSciNetCrossRefGoogle Scholar
  20. 20.
    A. H. Ghamarian, M. C. W. Geilen, S. Stuijk, T. Basten, B. D. Theelen, M. R. Mousavi, A. J. M. Moonen, and M. J. G. Bekooij. Throughput Analysis of Synchronous Data Flow Graphs. In Proceedings of the 6th International Conference on Application of Concurrency to System Design (ACSD), pages 25–36. IEEE, 2006.Google Scholar
  21. 21.
    A.H. Ghamarian, M. Geilen, T. Basten, B. Theelen, M.R. Mousavi, and S. Stuijk. Liveness and boundedness of synchronous data flow graphs. In Proceedings of the 6th conference on Formal Methods in Computer Aided Design (FMCAD), pages 68–75. IEEE, November 2006.Google Scholar
  22. 22.
    Amir Hossein Ghamarian. Timing analysis of synchronous data flow graphs. PhD thesis, Eindhoven University of Technology, The Netherlands, July 2008.Google Scholar
  23. 23.
    Steve Goddard. On the Management of Latency in the synthesis of real-time signal processing systems from processing graphs. PhD thesis, University of North Carolina at Chapel Hill, 1998.Google Scholar
  24. 24.
    S. Ha and H. Oh. Decidable signal processing dataflow graphs. In S. S. Bhattacharyya, E. F. Deprettere, R. Leupers, and J. Takala, editors, Handbook of Signal Processing Systems. Springer, third edition, 2018.Google Scholar
  25. 25.
    B. Heidergott, Geert Jan Olsder, and Jacob van der Woude. Max Plus at Work: modeling and analysis of synchronized systems. Princeton University Press, 2006.Google Scholar
  26. 26.
    K. Ito and K.K. Parhi. Determining the iteration bounds of single-rate and multi-rate data-flow graphs. In Proceedings of the 1994 Asia Pacific Conference on Circuits and Systems, pages 163–168. IEEE, 1994.Google Scholar
  27. 27.
    Richard M. Karp and James B. Orlin. Parametric shortest path algorithms with an application to cyclic staffing. Discrete Applied Mathematics, 3(1):37–45, February 1981.MathSciNetCrossRefGoogle Scholar
  28. 28.
    E.A. Lee and D.G. Messerschmitt. Synchronous data flow. Proceedings of the IEEE, 75(9):1235–1245, 1987.CrossRefGoogle Scholar
  29. 29.
    E.A. Lee and T.M. Parks. Dataflow process networks. Proceedings of the IEEE, 83(5):773–801, May 1995.CrossRefGoogle Scholar
  30. 30.
    R. Leupers, M. A. Aguilar, J. Castrillon, and W. Sheng. Software compilation techniques for heterogeneous embedded multi-core systems. In S. S. Bhattacharyya, E. F. Deprettere, R. Leupers, and J. Takala, editors, Handbook of Signal Processing Systems. Springer, third edition, 2018.Google Scholar
  31. 31.
    Olivier Marchetti and Alix Munier-Kordon. Minimizing Place Capacities of Weighted Event Graphs for Enforcing Liveness. Discrete Event Dynamic Systems, 18(1):91, 2008.MathSciNetCrossRefGoogle Scholar
  32. 32.
    Orlando Moreira and Henk Corporaal. Scheduling Real-Time Streaming Applications onto an Embedded Multiprocessor, volume 24 of Embedded Systems. Springer International Publishing, Cham, 2014.CrossRefGoogle Scholar
  33. 33.
    K.K. Parhi. Algorithm transformation techniques for concurrent processors. Proceedings of the IEEE, 77(12):1879–1895, 1989.CrossRefGoogle Scholar
  34. 34.
    T.M. Parks and E.A. Lee. Non-preemptive real-time scheduling of dataflow systems. In Acoustics, Speech, and Signal Processing, 1995. ICASSP-95., 1995 International Conference on, volume 5, pages 3235–3238. IEEE, 1995.Google Scholar
  35. 35.
    T.M. Parks, J.L. Pino, and E.A. Lee. A Comparison of Synchronous and Cyclo-static Dataflow. In Proceedings of the 29th Asilomar Conference on Signals, Systems and Computers, volume 1, pages 204–210. IEEE Comput. Soc. Press, 1995.Google Scholar
  36. 36.
    Raymond Reiter. Scheduling Parallel Computations. Journal of the ACM, 15(4):590–599, October 1968.CrossRefGoogle Scholar
  37. 37.
    Firew Siyoum, Marc Geilen, Orlando Moreira, and Henk Corporaal. Worst-case throughput analysis of real-time dynamic streaming applications. In Proceedings of the eighth IEEE/ACM/IFIP international conference on Hardware/software codesign and system synthesis - CODES+ISSS ’12, page 463, New York, New York, USA, October 2012. ACM Press.Google Scholar
  38. 38.
    Sundararajan Sriram and Shuvra S. Bhattacharyya. Embedded Multiprocessors: Scheduling and Synchronization. CRC Press, February 2009.CrossRefGoogle Scholar
  39. 39.
    Sander Stuijk, Marc Geilen, and Twan Basten. Throughput-Buffering Trade-Off Exploration for Cyclo-Static and Synchronous Dataflow Graphs. IEEE Transactions on Computers, 57(10):1331–1345, October 2008.MathSciNetCrossRefGoogle Scholar
  40. 40.
    Enrique Teruel, Piotr Chrzastowski-Wachtel, José Manuel Colom, and Manuel Silva. On Weighted T-Systems. Application and Theory of Petri Nets, pages 348–367, June 1992.Google Scholar
  41. 41.
    Maarten Wiggers, Marco Bekooij, Pierre Jansen, and Gerard Smit. Efficient computation of buffer capacities for multi-rate real-time systems with back-pressure. In Proceedings of the 4th international conference on Hardware/software codesign and system synthesis - CODES+ISSS ’06, page 10, New York, New York, USA, 2006. ACM Press.Google Scholar
  42. 42.
    M.H. Wiggers, M.J.G. Bekooij, and G.J.M. Smit. Efficient Computation of Buffer Capacities for Cyclo-Static Dataflow Graphs. In Proceedings of the 44th ACM/IEEE Design Automation Conference (DAC), pages 658–663. IEEE, 2007.Google Scholar
  43. 43.
    Neal E. Young, Robert E. Tarjant, and James B. Orlin. Faster parametric shortest path and minimum-balance algorithms. Networks, 21(2):205–221, mar 1991.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of Twente, Faculty of EEMCSEnschedeThe Netherlands

Personalised recommendations