Abstract
Real-time system design involves proving the schedulability of a set of tasks with hard timing and other constraints that should run on one or several cores. When those requirements are known at design time, it is possible to compute a fixed scheduling of tasks before deployment. This approach avoids the overhead induced by an online scheduler and allows the designer to verify the schedulability of the taskset design under normal and degraded conditions, such as core failures. In this context, we propose to solve the schedulability problem as a state space exploration problem. We represent the schedulings as partial functions that map each task to a core and a point in time. Partial functions can be efficiently encoded using a new variant of decision diagrams, called Map-Family Decision Diagrams (MFDDs). Our setting allows first to create the MFDD of all possible schedulings and then apply homomorphic operations directly on it, in order to obtain the schedulings that respect the constraints of the taskset.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Incidentally, as MFDDs are finite graphs, it follows that all encoded functions f have a finite domain \( dom (f) \subseteq A\), represented by the non-terminal nodes along an accepting path, even if A is infinite.
- 2.
References
Baro, J., Boniol, F., Cordovilla, M., Noulard, E., Pagetti, C.: Off-line (optimal) multiprocessor scheduling of dependent periodic tasks. In: Proceedings of the 27th Annual ACM Symposium on Applied Computing, pp. 1815–1820 (2012)
Behrmann, G., Larsen, K.G., Rasmussen, J.I.: Optimal scheduling using priced timed automata. SIGMETRICS Perform. Eval. Rev. 32(4), 34–40 (2005)
Bergman, D., Ciré, A.A., van Hoeve, W., Hooker, J.N.: Decision Diagrams for Optimization. Artificial Intelligence: Foundations, Theory, and Algorithms. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-319-42849-9
Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Comput. 35(8), 677–691 (1986)
Cire, A.A., van Hoeve, W.J.: Multivalued decision diagrams for sequencing problems. Oper. Res. 61(6), 1411–1428 (2013)
Couvreur, J.-M., Encrenaz, E., Paviot-Adet, E., Poitrenaud, D., Wacrenier, P.-A.: Data decision diagrams for petri net analysis. In: Esparza, J., Lakos, C. (eds.) ICATPN 2002. LNCS, vol. 2360, pp. 101–120. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-48068-4_8
David, A., Larsen, K.G., Legay, A., Mikucionis, M.: Schedulability of Herschel revisited using statistical model checking. Int. J. Softw. Tools Technol. Transfer 17(2), 187–199 (2015). https://doi.org/10.1007/s10009-014-0331-4
Guan, N., Gu, Z., Deng, Q., Gao, S., Yu, G.: Exact schedulability analysis for static-priority global multiprocessor scheduling using model-checking. In: Obermaisser, R., Nah, Y., Puschner, P., Rammig, F.J. (eds.) SEUS 2007. LNCS, vol. 4761, pp. 263–272. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75664-4_26
Hong, S., Kordon, F., Paviot-Adet, E., Evangelista, S.: Computing a hierarchical static order for decision diagram-based representation from P/T nets. Trans. Petri Nets Other Models Concurr. 5, 121–140 (2012)
Jensen, A.R., Lauritzen, L.B., Laursen, O.: Optimal task graph scheduling with binary decision diagrams (2004)
Korousic-Seljak, B.: Task scheduling policies for real-time systems. Microprocess. Microsyst. 18(9), 501–511 (1994)
Lehoczky, J.P., Sha, L., Ding, Y.: The rate monotonic scheduling algorithm: exact characterization and average case behavior. In: Real-Time Systems Symposium, pp. 166–171. IEEE Computer Society (1989)
Linard, A., Paviot-Adet, E., Kordon, F., Buchs, D., Charron, S.: polydd: towards a framework generalizing decision diagrams. In: Gomes, L., Khomenko, V., Fernandes, J.M. (eds.) International Conference on Application of Concurrency to System Design, pp. 124–133. IEEE Computer Society, New York (2010)
Mahadevan, S., Storgaard, M., Madsen, J., Virk, K.: ARTS: a system-level framework for modeling MPSoC components and analysis of their causality. In: International Symposium on Modeling, pp. 480–483. IEEE Computer Society (2005)
Nguyen, V.A., Hardy, D., Puaut, I.: Cache-conscious offline real-time task scheduling for multi-core processors. In: 29th Euromicro Conference on Real-time Systems (ECRTS 2017). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2017)
Puffitsch, W., Noulard, E., Pagetti, C.: Off-line mapping of multi-rate dependent task sets to many-core platforms. Real-Time Syst. 51(5), 526–565 (2015). https://doi.org/10.1007/s11241-015-9232-1
Racordon, D., Buchs, D.: Verifying multi-core schedulability with data decision diagrams. In: Crnkovic, I., Troubitsyna, E. (eds.) SERENE 2016. LNCS, vol. 9823, pp. 45–61. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45892-2_4
Yalcinkaya, B., Nasri, M., Brandenburg, B.B.: An exact schedulability test for non-preemptive self-suspending real-time tasks. In: Teich, J., Fummi, F. (eds.) Design, Automation & Test in Europe, pp. 1228–1233. IEEE (2019)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Racordon, D., Coet, A., Stachtiari, E., Buchs, D. (2020). Solving Schedulability as a Search Space Problem with Decision Diagrams. In: Aleti, A., Panichella, A. (eds) Search-Based Software Engineering. SSBSE 2020. Lecture Notes in Computer Science(), vol 12420. Springer, Cham. https://doi.org/10.1007/978-3-030-59762-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-59762-7_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-59761-0
Online ISBN: 978-3-030-59762-7
eBook Packages: Computer ScienceComputer Science (R0)