Abstract
Schedulers assign starting times to events in a system such that a set of constraints is met and system productivity is maximized. We characterize the scheduler behaviour for the case where decisions are made by comparing affine expressions of design parameters such as task workload, processing speed, robot travelling speed, or a controller’s rise and settling time. Deterministic schedulers can be extended with symbolic execution, to keep track of the affine conditions on the parameters for which the scheduling decisions are made. We introduce a divide-and-conquer algorithm that uses this information to determine parameter regions for which the same sequence of decisions is taken given a particular scenario. The results provide designers insight in the impact of parameter changes on the performance of their system. The exploration can also be executed with the KLEE symbolic execution engine of the LLVM tool chain to extract the same results. We show that the divide-and-conquer approach provides the results much faster than the generic symbolic execution engine of KLEE. The results allow visualization of the sensitivity to all parameter combinations. The results of our approach therefore provide more insight in the sensitivity to parameters.
- Rajeev Alur and David L. Dill. 1994. A theory of timed automata. Theoretical Computer Science 126, 2 (1994), 183--235. DOI:http://dx.doi.org/10.1016/0304-3975(94)90010-8Google Scholar
Digital Library
- Neil Audsley, Alan Burns, Mike Richardson, Ken Tindell, and Andy J. Wellings. 1993. Applying new scheduling theory to static priority pre-emptive scheduling. Software Engineering Journal 8, 5 (Sep. 1993), 284--292. DOI:http://dx.doi.org/10.1049/sej.1993.0034Google Scholar
- Enrico Bini and Giorgio C. Buttazzo. 2004. Schedulability analysis of periodic fixed priority systems. IEEE Trans. Comput. 53, 11 (Nov 2004), 1462--1473. DOI:http://dx.doi.org/10.1109/TC.2004.103Google Scholar
Digital Library
- Cristian Cadar, Daniel Dunbar, and Dawson Engler. 2008. KLEE: Unassisted and automatic generation of high-coverage tests for complex systems programs. In OSDI’08. USENIX Association, Berkeley, CA, USA, 209--224.Google Scholar
Digital Library
- Alessandro Cimatti, Luigi Palopoli, and Yusi Ramadian. 2008. Symbolic computation of schedulability regions using parametric timed automata. In 2008 Real-Time Systems Symposium (RTSS’08). IEEE, 80--89. DOI:http://dx.doi.org/10.1109/RTSS.2008.36Google Scholar
Digital Library
- Paul Feautrier. 1988. Parametric integer programming. RAIRO-Operations Research 22, 3 (1988), 243--268.Google Scholar
Cross Ref
- Paul Feautrier. 1992. Some efficient solutions to the affine scheduling problem. I. One-dimensional time. International Journal of Parallel Programming 21, 5 (1 Oct 1992), 313--347.Google Scholar
Digital Library
- Komei Fukuda and Alain Prodon. 1996. Double description method revisited. Combinatorics and Computer Science (1996), 91--111. DOI:http://dx.doi.org/10.1007/3-540-61576-8_77Google Scholar
- Paul Gastin, Sayan Mukherjee, and B. Srivathsan. 2018. Reachability in timed automata with diagonal constraints. In International Conference on Concurrency Theory (CONCUR’18).Google Scholar
- Amir Ghamarian, Marc Geilen, Twan Basten, and Sander Stuijk. 2008. Parametric throughput analysis of synchronous data flow graphs. In 2008 Design, Automation and Test in Europe (DATE’08). IEEE, 116--121. DOI:http://dx.doi.org/10.1109/DATE.2008.4484672Google Scholar
- Khaled R. Heloue, Sari Onaissi, and Farid N. Najm. 2012. Efficient block-based parameterized timing analysis covering all potentially critical paths. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD) 31, 4 (April 2012), 472--484. DOI:http://dx.doi.org/10.1109/TCAD.2011.2175392Google Scholar
Digital Library
- Thomas Hune, Judi Romijn, Mariëlle Stoelinga, and Frits Vaandrager. 2001. Linear parametric model checking of timed automata. In Tools and Algorithms for the Construction and Analysis of Systems (TACAS). Springer, Berlin, Heidelberg, 189--203. DOI:http://dx.doi.org/10.1016/S1567-8326(02)00037-1Google Scholar
- Mitra Nasri and Björn B. Brandenburg. 2017. An exact and sustainable analysis of non-preemptive scheduling. In 2017 IEEE Real-Time Systems Symposium (RTSS’17). IEEE, 12--23. DOI:http://dx.doi.org/10.1109/RTSS.2017.00009Google Scholar
Cross Ref
- Mitra Nasri, Geoffrey Nelissen, and Björn B. Brandenburg. 2018. A response-time analysis for non-preemptive job sets under global scheduling. In 2018 30th Euromicro Conference on Real-Time Systems (ECRTS), Vol. 106. 9--1.Google Scholar
- Krishnamurthy Subramani. 2001. Parametric scheduling - Algorithms and complexity. In High Performance Computing (HiPC 2001). Springer, Berlin, Heidelberg, 36--46.Google Scholar
Cross Ref
- Joost van Pinxten, Marc Geilen, Martijn Hendriks, and Twan Basten. 2018. Parametric critical path analysis for event networks with minimal and maximal time lags. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD) 37, 11 (2018), 2697--2708. DOI:http://dx.doi.org/10.1109/TCAD.2018.2857360Google Scholar
Cross Ref
- Umar Waqas, Marc Geilen, Jack Kandelaars, Lou Somers, Twan Basten, Sander Stuijk, Patrick Vestjens, and Henk Corporaal. 2015. A re-entrant flowshop heuristic for online scheduling of the paper path in a large scale printer. In 2015 Design, Automation and Test in Europe (DATE’15). IEEE, 573--578. DOI:http://dx.doi.org/10.7873/DATE.2015.0519Google Scholar
- Umar Waqas, Marc Geilen, Sander Stuijk, Joost van Pinxten, Twan Basten, Lou Somers, and Henk Corporaal. 2016. A fast estimator of performance with respect to the design parameters of self re-entrant flowshops. In Euromicro Conference on Digital System Design (DSD’16). IEEE, 215--221. DOI:http://dx.doi.org/10.1109/DSD.2016.26Google Scholar
Cross Ref
- Fengxiang Zhang and Alan Burns. 2009. Schedulability analysis for real-time systems with EDF scheduling. IEEE Trans. Comput. 58, 9 (2009), 1250--1258. DOI:http://dx.doi.org/10.1109/TC.2009.58Google Scholar
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Index Terms
Parametric Scheduler Characterization
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