Abstract
In this paper we approach the problem of Mixed Criticality (MC) for probabilistic real-time systems where tasks execution times are described with probabilistic distributions. In our analysis, the task enters high criticality mode if its response time exceeds a certain threshold, which is a slight deviation from a more classical approach in MC. We do this to obtain an application oriented MC system in which criticality mode changes depend on actual scheduled execution. This is in contrast to classical approaches which use task execution time to make criticality mode decisions, because execution time is not affected by scheduling while the response time is. We use a graph-based approach to seek for an optimal MC schedule by exploring every possible MC schedule the task set can have. The schedule we obtain minimizes the probability of the system entering high criticality mode. In turn, this aims at maximizing the resource efficiency by the means of scheduling without compromising the execution of the high criticality tasks and minimizing the loss of lower criticality functionality. The proposed approach is applied to test cases for validation purposes.
This work is also a result of the CISTER Research Unit (UID/CEC/04234), supported by FCT/MCTES (Portuguese Foundation for Science and Technology).
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.
The distribution function accumulates the probabilities in the intervals of discretization at the worst case, e.g. probabilities at execution times 0.2, 0.5, 0.7, etc. are accumulated the time 1.
- 2.
Same reasoning also applies to multiplication of probabilities, however the denominator 1 gets multiplied too.
References
Alahmad, B., Gopalakrishnan, S.: A risk-constrained Markov decision process approachto scheduling mixed-criticality job sets. In: Workshop on Mixed-Criticality Systems (2016)
Alahmad, B., Gopalakrishnan, S.: Risk-aware scheduling of dual criticality job systems using demand distributions. LITES 5(1), 01:1–01:30 (2018). https://doi.org/10.4230/LITES-v005-i001-a001
Baruah, S., Easwaran, A., Guo, Z.: Mc-fluid: Simplified and optimally quantified. In: 2015 IEEE Real-Time Systems Symposium, pp. 327–337, December 2015
Bucci, G., Carnevali, L., Ridi, L., Vicario, E.: Oris: a tool for modeling, verification and evaluation of real-time systems. Int. J. Softw. Tools Technol. Transf. 12(5), 391–403 (2010)
Burns, A., Davis, R.: Mixed criticality systems - a review, 12th edn. Technical report, Department of CS, U. of York, UK, March 2019
Cucu-Grosjean, L.: Independence - a misunderstood property of and for (probabilistic) real-time systems. In: Real-Time Systems: the Past, the Present and the Future (2013)
Davis, R.I., Burns, A., Griffin, D.: On the meaning of pWCET distributions and their use in schedulability analysis. In: In Proceedings Real-Time Scheduling Open Problems Seminar at ECRTS (2017)
Guo, Z., Santinelli, L., Yang, K.: EDF schedulability analysis on mixed-criticality systems with permitted failure probability. In: Proceedings of the RTCSA (2015)
Huang, H., Gill, C., Lu, C.: Mcflow: a real-time multi-core aware middleware for dependent task graphs. In: 2012 IEEE International Conference on Embedded and Real-Time Computing Systems and Applications, pp. 104–113, August 2012
Huang, S., Zhu, Y., Duan, J.: A new scheduling approach for mix-criticality real-time system. In: 2013 Fourth International Conference on Intelligent Control and Information Processing (ICICIP), pp. 43–46, June 2013
Kahil, R., Socci, D., Poplavko, P., Bensalem, S.: Algorithmic complexity of correctness testing in MC-scheduling. In: Proceedings of the 26th International Conference on Real-Time Networks and Systems, RTNS 2018, Chasseneuil-du-Poitou, France, 10–12 October 2018, pp. 180–190. ACM (2018)
Kim, K., Diaz, J., Lo Bello, L., Lopez, J., Lee, C.G., Min, S.L.: An exact stochastic analysis of priority-driven periodic real-time systems and its approximations. IEEE Trans. Comput. 54(11), 1460–1466 (2005)
Li, H., Baruah, S.: An algorithm for scheduling certifiable mixed-criticality sporadic task systems. In: Proceedings of the 2010 31st IEEE Real-Time Systems Symposium, RTSS 2010, pp. 183–192. IEEE Computer Society, Washington, DC (2010). https://doi.org/10.1109/RTSS.2010.18
Maxim, D., Davis, R.I., Cucu-Grosjean, L., Easwaran, A.: Probabilistic analysis for mixed criticality systems using fixed priority preemptive scheduling. In: Proceedings of the 25th International Conference on Real-Time Networks and Systems, RTNS 2017, pp. 237–246. ACM, New York (2017). http://doi.acm.org/10.1145/3139258.3139276
Nélis, V., Yomsi, P.M., Pinho, L.M., Fonseca, J., Bertogna, M., Quiñones, E., Vargas, R., Marongiu, A.: The challenge of time-predictability in modern many-core architectures. In: 14th International Workshop on Worst-Case Execution Time Analysis (2014)
Santinelli, L., George, L.: Probabilities and mixed-criticalities: the probabilistic C-space. In: 3rd International Workshop on Mixed Criticality Systems WMC at RTSS (2016)
Santinelli, L., Guet, F., Morio, J.: Revising measurement-based probabilistic timing analysis. In: 2017 IEEE Real-Time and Embedded Technology and Applications Symposium, RTAS 2017, Pittsburg, PA, USA, 18–21 April 2017, pp. 199–208 (2017)
Santinelli, L., Meumeu Yomsy, P., Maxim, D., Cucu-Grosjean, L.: A component-based framework for modeling and analysing probabilistic real-time systems. In: 16th IEEE International Conference on Emerging Technologies and Factory Automation (2011)
Singh, J., Santinelli, L., Infantes, G., Doose, D., Brunel, J.: Mixed criticality probabilistic real-time systems analysis using discrete time Markov chain. In: 6th International Workshop on Mixed Criticality Systems (WMC) (2018)
Stigge, M., Ekberg, P., Guan, N., Yi, W.: The digraph real-time task model. In: Proceedings of the 2011 17th IEEE Real-Time and Embedded Technology and Applications Symposium, RTAS 2011, pp. 71–80. IEEE Computer Society, Washington, DC (2011). https://doi.org/10.1109/RTAS.2011.15
Soong, T.: Fundamentals of probability and statistics for engineers, p. 391, January 2004. ISBN 9780470868157
Vestal, S.: Preemptive scheduling of multi-criticality systems with varying degrees of execution time assurance. In: Proceedings of the 28th IEEE International Real-Time Systems Symposium (RTSS), pp. 239–243. IEEE Computer Society (2007)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Singh, J., Santinelli, L., Reghenzani, F., Bletsas, K., Doose, D., Guo, Z. (2019). Mixed Criticality Scheduling of Probabilistic Real-Time Systems. In: Guan, N., Katoen, JP., Sun, J. (eds) Dependable Software Engineering. Theories, Tools, and Applications. SETTA 2019. Lecture Notes in Computer Science(), vol 11951. Springer, Cham. https://doi.org/10.1007/978-3-030-35540-1_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-35540-1_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-35539-5
Online ISBN: 978-3-030-35540-1
eBook Packages: Computer ScienceComputer Science (R0)