Schedulability of Herschel-Planck Revisited Using Statistical Model Checking

  • Alexandre David
  • Kim Guldstrand Larsen
  • Axel Legay
  • Marius Mikučionis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7610)


Schedulability analysis is a main concern for several embedded applications due to their safety-critical nature. The classical method of response time analysis provides an efficient technique used in industrial practice. However, the method is based on conservative assumptions related to execution and blocking times of tasks. Consequently, the method may falsely declare deadline violations that will never occur during execution. This paper is a continuation of previous work of the authors in applying extended timed automata model checking (using the tool UPPAAL) to obtain more exact schedulability analysis, here in the presence of non-deterministic computation times of tasks given by intervals [BCET,WCET]. Considering computation intervals makes the schedulability of the resulting task model undecidable. Our contribution is to propose a combination of model checking techniques to obtain some guarantee on the (un)schedulability of the model even in the presence of undecidability.

Two methods are considered: symbolic model checking and statistical model checking. Symbolic model checking allows to conclude schedulability – i.e. absence of deadline violations – for varying sizes of BCET. However, the symbolic model checking technique is over-approximating for the considered task model and can therefore not be used for disproving schedulability. As a remedy, we show how statistical model checking may be used to generate concrete counter examples witnessing non-schedulability. In addition, we apply statistical model checking to obtain more informative performance analysis – e.g. expected response times – when the system is schedulable.

The methods are demonstrated on a complex satellite software system yielding new insights useful for the company.


Model Check Response Time Distribution Schedulability Analysis Symbolic Model Check Response Time Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BACC+98]
    Ben-Abdallah, H., Choi, J.-Y., Clarke, D., Kim, Y.S., Lee, I., Xie, H.-L.: A process algebraic approach to the schedulability analysis of real-time systems. Real-Time Systems 15, 189–219 (1998), doi:10.1023/A:1008047130023CrossRefGoogle Scholar
  2. [BDL+12]
    Bulychev, P., David, A., Guldstrand Larsen, K., Legay, A., Mikučionis, M., Bøgsted Poulsen, D.: Checking and Distributing Statistical Model Checking. In: Goodloe, A.E., Person, S. (eds.) NFM 2012. LNCS, vol. 7226, pp. 449–463. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. [BHK99]
    Bradley, S., Henderson, W., Kendall, D.: Using timed automata for response time analysis of distributed real-time systems. In: Systems in 24th IFAC/IFIP Workshop on Real-Time Programming, WRTP 1999, pp. 143–148 (1999)Google Scholar
  4. [BHK+04]
    Bohnenkamp, H.C., Hermanns, H., Klaren, R., Mader, A., Usenko, Y.S.: Synthesis and stochastic assessment of schedules for lacquer production. In: Proceedings of the First International Conference on the Quantitative Evaluation of Systems, QEST 2004, pp. 28–37 (September 2004)Google Scholar
  5. [BHM09]
    Brekling, A., Hansen, M.R., Madsen, J.: Moves – a framework for modelling and verifying embedded systems. In: International Conference on Microelectronics, ICM 2009, pp. 149–152 (December 2009)Google Scholar
  6. [Bur94]
    Burns, A.: Preemptive priority based scheduling: An appropriate engineering approach. In: Principles of Real-Time Systems, pp. 225–248. Prentice Hall (1994)Google Scholar
  7. [DILS10]
    David, A., Illum, J., Larsen, K.G., Skou, A.: Model-Based Framework for Schedulability Analysis Using UPPAAL 4.1. In: Nicolescu, G., Mosterman, P.J. (eds.) Model-Based Design for Embedded Systems, pp. 93–119. CRC Press (2010)Google Scholar
  8. [DLL+11a]
    David, A., Larsen, K.G., Legay, A., Mikučionis, M., Bøgsted Poulsen, D., van Vliet, J., Wang, Z.: Statistical Model Checking for Networks of Priced Timed Automata. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 80–96. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. [DLL+11b]
    David, A., Larsen, K.G., Legay, A., Mikučionis, M., Wang, Z.: Time for Statistical Model Checking of Real-Time Systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 349–355. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. [FKPY07]
    Fersman, E., Krcal, P., Pettersson, P., Yi, W.: Task automata: Schedulability, decidability and undecidability. Information and Computation 205(8), 1149–1172 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  11. [JP86]
    Joseph, M., Pandya, P.K.: Finding response times in a real-time system. Comput. J. 29(5), 390–395 (1986)MathSciNetCrossRefGoogle Scholar
  12. [KZH+09]
    Katoen, J.-P., Zapreev, I.S., Moritz Hahn, E., Hermanns, H., Jansen, D.N.: The ins and outs of the probabilistic model checker MRMC. In: Proc. of 6th Int. Conference on the Quantitative Evaluation of Systems (QEST), pp. 167–176. IEEE Computer Society (2009)Google Scholar
  13. [LDB10]
    Legay, A., Delahaye, B., Bensalem, S.: Statistical Model Checking: An Overview. In: Barringer, H., Falcone, Y., Finkbeiner, B., Havelund, K., Lee, I., Pace, G., Roşu, G., Sokolsky, O., Tillmann, N. (eds.) RV 2010. LNCS, vol. 6418, pp. 122–135. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. [MLR+10]
    Mikučionis, M., Larsen, K.G., Rasmussen, J.I., Nielsen, B., Skou, A., Palm, S.U., Pedersen, J.S., Hougaard, P.: Schedulability Analysis Using Uppaal: Herschel-Planck Case Study. In: Margaria, T., Steffen, B. (eds.) ISoLA 2010, Part II. LNCS, vol. 6416, pp. 175–190. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. [SLC06]
    Sokolsky, O., Lee, I., Clarke, D.: Schedulability analysis of aadl models. In: 20th International Parallel and Distributed Processing Symposium, IPDPS 2006, p. 8 (April 2006)Google Scholar
  16. [SVA04]
    Sen, K., Viswanathan, M., Agha, G.: Statistical Model Checking of Black-Box Probabilistic Systems. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 202–215. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. [YS06]
    Håkan, L., Younes, S., Simmons, R.G.: Statistical probabilistic model checking with a focus on time-bounded properties. Inf. Comput. 204(9), 1368–1409 (2006)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexandre David
    • 1
  • Kim Guldstrand Larsen
    • 1
  • Axel Legay
    • 2
  • Marius Mikučionis
    • 1
  1. 1.Computer ScienceAalborg UniversityDenmark
  2. 2.INRIA/IRISARennes CedexFrance

Personalised recommendations