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Back to basics: Homogeneous representations of multi-rate synchronous dataflow graphs

Published: 01 October 2013 Publication History

Abstract

Exact temporal analyses of multi-rate synchronous dataflow (MRSDF) graphs, such as computing the maximum achievable throughput, or sufficient buffer sizes required to reach a minimum throughput, require a homogeneous representation called a homogeneous synchronous dataflow (HSDF) graph. The size of such an HSDF graph may, in the worst case, be exponential in the size of the MRSDF graph. In this paper, we revisit the transformation from MRSDF to HSDF, and show how this transformation may be done either exactly or approximately. The approximate transformation gives both an optimistic and a pessimistic HSDF graph, each of which has the same size as the MRSDF graph. We furthermore show how strict lower and upper bounds on throughput, or on the buffer sizes required to reach a minimum throughput, may be obtained from these approximating graphs.

References

[1]
E. Lee and D. Messerschmitt, "Synchronous data flow," Proceedings of the IEEE, vol. 75, no. 9, pp. 1235-1245, 1987.
[2]
S. Sriram and S. S. Bhattacharyya, Embedded multiprocessors: Scheduling and synchronization. CRC press, 2009.
[3]
A. H. Ghamarian, M. C. W. Geilen, S. Stuijk, T. Basten, A. J. M. Moonen, M. Bekooij, B. Theelen, and M. Mousavi, "Throughput analysis of synchronous data flow graphs," in Proceedings of the 6th International Conference on Application of Concurrency to System Design (ACSD). IEEE Computer Society Press, Los Alamitos, CA, USA, Jun. 2006, pp. 25-36.
[4]
J. P. Hausmans, S. J. Geuns, M. H. Wiggers, and M. J. Bekooij, "Compositional temporal analysis model for incremental hard real-time system design," in Proceedings of the tenth ACM international conference on Embedded software - EMSOFT '12. New York, New York, USA: ACM Press, Oct. 2012, p. 185.
[5]
M. H. Wiggers, "Aperiodic Multiprocessor Scheduling for Real-Time Stream Processing Applications," Ph.D. dissertation, University of Twente, Enschede, The Netherlands, Jun. 2009.
[6]
S. Stuijk, M. C. W. Geilen, and T. Basten, "SDF3: SDF For Free," in Proceedings on the 6th International Conference on Application of Concurrency to System Design (ACSD). IEEE Computer Society Press, Los Alamitos, CA, USA, Jun. 2006, pp. 276-278.
[7]
O. Marchetti and A. Munier-Kordon, "Complexity results for Weighted Timed Event Graphs," Discrete Optimization, vol. 7, no. 3, pp. 166-180, Aug. 2010.
[8]
G. Cohen, S. Gaubert, and J. Quadrat, "Timed-event graphs with multipliers and homogeneous min-plus systems," IEEE Transactions on Automatic Control, vol. 43, no. 9, pp. 1296-1302, 1998.
[9]
E. Teruel, P. Chrzastowski-Wachtel, J. M. Colom, and M. Silva, "On Weighted T-Systems," Lecture Notes In Computer Science; Vol. 616, p. 348, 1992.
[10]
G. Cohen, G. J. Olsder, and J.-p. Quadrat, Synchronization and linearity. Wiley New York, 1992.
[11]
M. Geilen, "Reduction techniques for synchronous dataflow graphs," Annual ACM IEEE Design Automation Conference, pp. 911-916, 2009.
[12]
R. de Groote, J. Kuper, H. Broersma, and G. J. Smit, "Max-Plus Algebraic Throughput Analysis of Synchronous Dataflow Graphs," in 2012 38th Euromicro Conference on Software Engineering and Advanced Applications. IEEE, Sep. 2012, pp. 29-38.
[13]
K. Ito and K. K. Parhi, "Determining the minimum iteration period of an algorithm," Journal of VLSI Signal Processing, vol. 11, no. 3, pp. 229-244, Dec. 1995.
[14]
M. Nakamura and M. Silva, "Cycle time computation in deterministically timed weighted marked graphs," in 1999 7th IEEE International Conference on Emerging Technologies and Factory Automation. Proceedings ETFA '99 (Cat. No. 99TH8467), vol. 2. IEEE, pp. 1037-1046.
[15]
A. Dasdan, "Experimental analysis of the fastest optimum cycle ratio and mean algorithms," ACM Transactions on Design Automation of Electronic Systems (TODAES), vol. 9, no. 4, p. 385, 2004.
[16]
J. Cochet-terrasson, G. Cohen, S. Gaubert, M. M. Gettrick, and J.-P. Quadrat, "Numerical Computation of Spectral Elements in Max-Plus Algebra," in Proceedings of the IFAC Conference on System Structure and Control, Jul. 1998.
[17]
B. Heidergott, G. J. Olsder, and J. van der Woude, Max Plus at Work: modeling and analysis of synchronized systems. Princeton University Press, 2006.
[18]
N. Young, R. Tarjan, and J. Orlin, "Faster Parametric Shortest Path and Minimum Balance Algorithms," ArXiv Computer Science e-prints, May 2002.
[19]
R. Karp, "Parametric shortest path algorithms with an application to cyclic staffing," Discrete Applied Mathematics, vol. 3, no. 1, pp. 37-45, Feb. 1981.
[20]
M. Geilen, "Synchronous dataflow scenarios," ACM Transactions on Embedded Computing Systems, vol. 10, no. 2, pp. 1-31, Dec. 2010.
[21]
M. Geilen, S. Tripakis, and M. Wiggers, "The earlier the better," in Proceedings of the 14th international conference on Hybrid systems: computation and control - HSCC '11. New York, New York, USA: ACM Press, Apr. 2011, p. 23.
[22]
A. Ghamarian, M. Geilen, T. Basten, B. Theelen, M. Mousavi, and S. Stuijk, "Liveness and boundedness of synchronous data flow graphs," FMCAD06, no. August, pp. 68-75, 2006.
[23]
G. Cohen, S. Gaubert, and J.-P. Quadrat, "Max-plus algebra and system theory: Where we are and where to go now," Annual Reviews in Control, vol. 23, pp. 207-219, Jan. 1999.
[24]
J. Pino, S. Bhattacharyya, and E. Lee, "A hierarchical multiprocessor scheduling system for DSP applications," in Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers, vol. 1. IEEE Comput. Soc. Press, pp. 122-126.
[25]
S. Tripakis, D. Bui, B. Rodiers, and E. A. Lee, "Compositionality in Synchronous Data Flow," in Proceedings of the 1st ACM/IEEE International Conference on Cyber-Physical Systems - ICCPS '10. New York, New York, USA: ACM Press, Apr. 2010, p. 199.
[26]
S. Stuijk, M. Geilen, and T. Basten, "Exploring trade-offs in buffer requirements and throughput constraints for synchronous dataflow graphs," in Proceedings of the 43rd annual conference on Design automation - DAC '06. New York, New York, USA: ACM Press, Jul. 2006, p. 899.
[27]
G. Bilsen, M. Engels, R. Lauwereins, and J. Peperstraete, "Cyclo-static data flow," in Acoustics, Speech, and Signal Processing, 1995. ICASSP-95., 1995 International Conference on, vol. 5, 1995, pp. 3255-3258 vol. 5.

Cited By

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  • (2017)Hybrid Latency Minimization Approach using Model Checking and Dataflow AnalysisProceedings of the 20th International Workshop on Software and Compilers for Embedded Systems10.1145/3078659.3078665(41-50)Online publication date: 12-Jun-2017
  • (2017)Throughput Propagation in Constraint-Based Design Space Exploration for Mixed-Criticality SystemsProceedings of the 9th Workshop on Rapid Simulation and Performance Evaluation: Methods and Tools10.1145/3023973.3023977(1-8)Online publication date: 23-Jan-2017
  • (2014)Unified dataflow model for the analysis of data and pipeline parallelism, and buffer sizingProceedings of the Twelfth ACM/IEEE Conference on Formal Methods and Models for Codesign10.1109/MEMCOD.2014.6961839(12-21)Online publication date: 1-Oct-2014

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cover image ACM Conferences
MEMOCODE '13: Proceedings of the Eleventh ACM/IEEE International Conference on Formal Methods and Models for Codesign
October 2013
194 pages
ISBN:9781479909056

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Published: 01 October 2013

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Overall Acceptance Rate 34 of 82 submissions, 41%

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View all
  • (2017)Hybrid Latency Minimization Approach using Model Checking and Dataflow AnalysisProceedings of the 20th International Workshop on Software and Compilers for Embedded Systems10.1145/3078659.3078665(41-50)Online publication date: 12-Jun-2017
  • (2017)Throughput Propagation in Constraint-Based Design Space Exploration for Mixed-Criticality SystemsProceedings of the 9th Workshop on Rapid Simulation and Performance Evaluation: Methods and Tools10.1145/3023973.3023977(1-8)Online publication date: 23-Jan-2017
  • (2014)Unified dataflow model for the analysis of data and pipeline parallelism, and buffer sizingProceedings of the Twelfth ACM/IEEE Conference on Formal Methods and Models for Codesign10.1109/MEMCOD.2014.6961839(12-21)Online publication date: 1-Oct-2014

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