Abstract
Synchronous data flow graphs (SDFGs) are widely used to model digital signal processing and streaming media applications. In this paper, we present exact methods for static optimal scheduling and mapping of SDFGs on a heterogenous multiprocessor platform. The optimization criteria we consider are throughput and energy consumption, taking into account the combination of various constraints such as auto-concurrency and buffer sizes. We present a concise and flexible (priced) timed automata semantics of system models, which include an SDFG and a multiprocessor platform, and formulate the optimization goals as temporal logic formulas. The optimization and scheduling problems are then transformed to model checking problems, which are solved by UPPAAL (CORA). Thanks to the exhaustive exploration nature of model checking and the facility of the tools, we obtain two pareto-optimal schedules, one with an optimal throughput and a best energy consumption and another with an optimal energy consumption and a best throughput. The approach is applied to two real applications with different parameters. The case studies show that our approach can deal with moderate models within reasonable execution time and reveal the impacts of different constraints on optimization goals.
This work is partially supported by National Key Basic Research Program of China (973 program) (No. 2014CB340701) and the National Natural Science Foundation of China (Nos. 61472406, 61472474, 61272135, 61361136002 and U1435220).
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Abdeddaïm, Y., Asarin, E., Maler, O., et al.: Scheduling with timed automata. Theor. Comput. Sci. 354(2), 272–300 (2006)
Adé, M., Lauwereins, R., Peperstraete, J.: Data memory minimisation for synchronous data flow graphs emulated on DSP-FPGA targets. In: Proc. of the 34th Ann. Design Automation Conf (DAC), pp. 64–69 (1997)
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)
Behrmann, G., Larsen, K.G., Rasmussen, J.I.: Priced timed automata: Algorithms and applications. In: de Boer, F.S., Bonsangue, M.M., Graf, S., de Roever, W.-P. (eds.) FMCO 2004. LNCS, vol. 3657, pp. 162–182. Springer, Heidelberg (2005)
Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N.: Quantitative analysis of real-time systems using priced timed automata. Comm. of the ACM 54(9), 78–87 (2011)
Cimatti, A., Clarke, E., Giunchiglia, F., Roveri, M.: NuSMV: a new symbolic model checker. International Journal on Software Tools for Technology Transfer 2(4), 410–425 (2000)
Fakih, M., Grüttner, K., Fränzle, M., Rettberg, A.: Towards performance analysis of SDFGs mapped to shared-bus architectures using model-checking. In: Proc. of the Conference on Design, Automation and Test in Europe, pp. 1167–1172 (2013)
Fersman, E., Mokrushin, L., Pettersson, P., Yi, W.: Schedulability analysis of fixed-priority systems using timed automata. Theor. Comput. Sci. 354(2), 301 (2006)
Geilen, M., Basten, T., Stuijk, S.: Minimising buffer requirements of synchronous dataflow graphs with model checking. In: Proc. of the 42nd Annu. Design Automation Conf. (DAC) (2005)
Gu, Z., Yuan, M., Guan, N., Lv, M., He, X., Deng, Q., Yu, G.: Static scheduling and software synthesis for dataflow graphs with symbolic model-checking. In: Proc. of 28th International Real-Time Systems Symposium (RTSS), pp. 353–364 (2007)
Harbour, M.G., Klein, M.H., Lehoczky, J.P.: Timing analysis for fixed-priority scheduling of hard real-time systems. IEEE Trans. on Soft. Eng. 20(1), 13–28 (1994)
Hartel, P.H., Ruys, T.C., Geilen, M.C.: Scheduling optimisations for SPIN to minimise buffer requirements in synchronous data flow. In: Proc of the International Conference on Formal Methods in Computer-Aided Design, p. 21 (2008)
Hirzel, M., Soulé, R., Schneider, S., Gedik, B., Grimm, R.: A catalog of stream processing optimizations. ACM Comput. Surv. 46(4), 46:1–46:34 (2014)
Holzmann, G.J.: The model checker SPIN. IEEE Transactions on Software Engineering 23(5), 279–295 (1997)
Larsen, K.G., Pettersson, P., Yi, W.: UPPAAL in a nutshell. International Journal on Software Tools for Technology Transfer (STTT) 1(1), 134–152 (1997)
Lee, E., Messerschmitt, D.: Static scheduling of synchronous data flow programs for digital signal processing. IEEE Trans. Comput. 36(1), 24–35 (1987)
Madsen, J., Hansen, M.R., Knudsen, K.S., Nielsen, J.E., Brekling, A.W.: System-level verification of multi-core embedded systems using timed-automata. In: Proc. of the 17th World Congress International Federation of Automatic Control, Seoul, Korea, pp. 9302–9307 (2008)
Malik, A., Gregg, D.: Orchestrating stream graphs using model checking. ACM Trans. Archit. Code Optim. 10(3), 19:1–19:25 (2013)
Parhi, K.K., Messerschmitt, D.G.: Static rate-optimal scheduling of iterative data-flow programs via optimum unfolding. IEEE Trans. Comput. 40(2), 178–195 (1991)
Singh, A.K., Shafique, M., Kumar, A., Henkel, J.: Mapping on multi/many-core systems: Survey of current and emerging trends. In: Proc. of the 50th Ann. Design Automation Conf. (DAC), p. 1 (2013)
Sriram, S., Bhattacharyya, S.S.: Embedded multiprocessors: scheduling and synchronization. CRC Press (2009)
Stuijk, S., Geilen, M., Basten, T.: Throughput-buffering trade-off exploration for cyclo-static and synchronous dataflow graphs. IEEE Trans. Comput. 57(10), 1331–1345 (2008)
Theelen, B., Katoen, J.P., Wu, H.: Model checking of scenario-aware dataflow with CADP. In: Proceedings of the Conference on Design, Automation and Test in Europe, pp. 653–658 (2012)
Zhu, X.-Y., Geilen, M., Basten, T., Stuijk, S.: Static rate-optimal scheduling of multirate DSP algorithms via retiming and unfolding. In: Proc. of the 18th Real-Time and Embedded Technology and Applications Symposium (RTAS), pp. 109–118 (2012)
Zivojnovic, V., Ritz, S., Meyr, H.: Optimizing DSP programs using the multirate retiming transformation. Proc. EUSIPCO Signal Process. VII, Theories Applicat. (1994)
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Zhu, XY., Yan, R., Gu, YL., Zhang, J., Zhang, W., Zhang, G. (2015). Static Optimal Scheduling for Synchronous Data Flow Graphs with Model Checking. In: Bjørner, N., de Boer, F. (eds) FM 2015: Formal Methods. FM 2015. Lecture Notes in Computer Science(), vol 9109. Springer, Cham. https://doi.org/10.1007/978-3-319-19249-9_34
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DOI: https://doi.org/10.1007/978-3-319-19249-9_34
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