Skip to main content

Abstract

Wireless systems such as satellites and sensor networks are often battery-powered. To operate optimally they must therefore take the performance properties of real batteries into account. Additionally, these systems, and therefore their batteries, are often exposed to loads with uncertain timings. Mixed criticality and soft real-time systems may accept deadline violations and therefore enable trade-offs and evaluation of performance by criteria such as the number of tasks that can be completed with a given battery. We model a task set in combination with the kinetic battery model as a stochastic hybrid system and study its performance under battery-aware scheduling strategies. We believe that this evaluation does not scale with current verification techniques for stochastic hybrid systems. Instead statistical model checking provides a viable alternative with statistical guarantees. Based on our model we also calculate an upper bound on the attainable number of task instances from a battery, and we provide a battery-aware scheduler that wastes no energy on instances that are not guaranteed to make their deadlines.

This work is partially supported by SENSATION (Self Energy-Supporting Autonomous Computation) under the EU’s Seventh Framework Programme.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abate, A., Katoen, J.P., Lygeros, J., Prandini, M.: Approximate model checking of stochastic hybrid systems. European Journal of Control 16, 624–641 (2010), http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=3711

    Article  MathSciNet  MATH  Google Scholar 

  2. Abate, A., Prandini, M., Lygeros, J., Sastry, S.: Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems. Automatica 44(11), 2724–2734 (2008), http://dx.doi.org/10.1016/j.automatica.2008.03.027

    Article  MathSciNet  MATH  Google Scholar 

  3. Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theor. Comput. Sci. 138(1), 3–34 (1995)

    Article  MATH  Google Scholar 

  4. Alur, R.: Formal verification of hybrid systems. In: Proceedings of the Ninth ACM International Conference on Embedded Software, EMSOFT 2011, pp. 273–278. ACM, New York (2011), http://doi.acm.org/10.1145/2038642.2038685

    Google Scholar 

  5. Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bartocci, E., Bortolussi, L. (eds.): Proceedings First International Workshop on Hybrid Systems and Biology, HSB 2012, Newcastle Upon Tyne, UK, September 3. EPTCS, vol. 92 (2012)

    Google Scholar 

  7. Behrmann, G., Fehnker, A., Hune, T., Larsen, K.G., Pettersson, P., Romijn, J., Vaandrager, F.W.: Minimum-cost reachability for priced timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 147–161. Springer, Heidelberg (2001)

    Google Scholar 

  8. Blom, H., Lygeros, J.: Stochastic Hybrid Systems: Theory and Safety Critical Applications, vol. 337 (2006)

    Google Scholar 

  9. Bouyer, P., Brihaye, T., Bruyère, V., Raskin, J.F.: On the optimal reachability problem of weighted timed automata. Formal Methods in System Design 31(2), 135–175 (2007)

    Article  MATH  Google Scholar 

  10. Bouyer, P., Brinksma, E., Larsen, K.G.: Optimal infinite scheduling for multi-priced timed automata. Formal Methods in System Design 32(1), 3–23 (2008)

    Article  MATH  Google Scholar 

  11. David, A., Du, D., Larsen, K.G., Legay, A., Mikucionis, M., Poulsen, D.B., Sedwards, S.: Statistical model checking for stochastic hybrid systems. In: Bartocci, Bortolussi (eds.) [6], pp. 122–136

    Google Scholar 

  12. David, A., Du, D., Larsen, K.G., Mikucionis, M., Skou, A.: An evaluation framework for energy aware buildings using statistical model checking. Science China Information Sciences 55(12), 2694–2707 (2012)

    Article  Google Scholar 

  13. 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)

    Chapter  Google Scholar 

  14. David, A., Larsen, K.G., Legay, A., Mikučionis, M., Poulsen, D.B., 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)

    Chapter  Google Scholar 

  15. 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), http://dl.acm.org/citation.cfm?id=2032305.2032332

    Chapter  Google Scholar 

  16. Hahn, E., Hartmanns, A., Hermanns, H., Katoen, J.P.: A compositional modelling and analysis framework for stochastic hybrid systems. Formal Methods in System Design 43(2), 191–232 (2013), http://dx.doi.org/10.1007/s10703-012-0167-z

    Article  MATH  Google Scholar 

  17. Henzinger, T.A.: The theory of hybrid automata. In: Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science, LICS 1996, pp. 278–292. IEEE Computer Society, Washington, DC (1996)

    Google Scholar 

  18. Jongerden, M.R., Haverkort, B.R.: Which battery model to use? IET Software 3(6), 445–457 (2009)

    Article  Google Scholar 

  19. Jongerden, M.R., Haverkort, B.R., Bohnenkamp, H.C., Katoen, J.P.: Maximizing system lifetime by battery scheduling. In: DSN. IEEE (2009)

    Google Scholar 

  20. Larsen, K.G.: Statistical model checking, refinement checking, optimization, … for stochastic hybrid systems. In: Jurdziński, M., Ničković, D. (eds.) FORMATS 2012. LNCS, vol. 7595, pp. 7–10. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  21. Manwell, J.F., McGowan, J.G.: Lead acid battery storage model for hybrid energy systems. Solar Energy 50(5), 399–405 (1993)

    Article  Google Scholar 

  22. Martins, J., Platzer, A., Leite, J.: Statistical model checking for distributed probabilistic-control hybrid automata with smart grid applications. In: Qin, S., Qiu, Z. (eds.) ICFEM 2011. LNCS, vol. 6991, pp. 131–146. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  23. 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)

    Chapter  Google Scholar 

  24. Pulungan, R., Hermanns, H.: Effective minimization of acyclic phase-type representations. In: Al-Begain, K., Heindl, A., Telek, M. (eds.) ASMTA 2008. LNCS, vol. 5055, pp. 128–143. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  25. Zhang, L., She, Z., Ratschan, S., Hermanns, H., Hahn, E.M.: Safety verification for probabilistic hybrid systems. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 196–211. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  26. Zuliani, P., Platzer, A., Clarke, E.M.: Bayesian statistical model checking with application to Stateflow/Simulink verification. Formal Methods in System Design 43(2), 338–367 (2013)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wognsen, E.R., Hansen, R.R., Larsen, K.G. (2014). Battery-Aware Scheduling of Mixed Criticality Systems. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation. Specialized Techniques and Applications. ISoLA 2014. Lecture Notes in Computer Science, vol 8803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45231-8_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-45231-8_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-45230-1

  • Online ISBN: 978-3-662-45231-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics