Probabilistic Model Checking for Energy-Utility Analysis

  • Christel Baier
  • Clemens Dubslaff
  • Joachim Klein
  • Sascha Klüppelholz
  • Sascha Wunderlich

Abstract

In the context of a multi-disciplinary project, where we contribute with formal methods for reasoning about energy-awareness and other quantitative aspects of low-level resource management protocols, we made a series of interesting observations on the strengths and limitations of probabilistic model checking. To our surprise, the operating-system experts identified several relevant quantitative measures that are not supported by state-of-the-art probabilistic model checkers. Most notably are conditional probabilities and quantiles. Both are standard in mathematics and statistics, but research on them in the context of probabilistic model checking is rare. Another deficit of standard probabilistic model-checking techniques was the lack of methods for establishing properties imposing constraints on the energy-utility ratio.

In this article, we will present formalizations of the above mentioned quantitative measures, illustrate their significance by means of examples and sketch computation methods that we developed in our recent work.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andrés, M.: Quantitative Analysis of Information Leakage in Probabilistic and Nondeterministic Systems. PhD thesis, UB Nijmegen (2011)Google Scholar
  2. 2.
    Andrés, M., van Rossum, P.: Conditional probabilities over probabilistic and nondeterministic systems. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 157–172. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Baier, C., Cloth, L., Haverkort, B., Hermanns, H., Katoen, J.-P.: Performability assessment by model checking of Markov reward models. Formal Methods in System Design 36(1), 1–36 (2010)CrossRefMATHGoogle Scholar
  4. 4.
    Baier, C., Daum, M., Dubslaff, C., Klein, J., Klüppelholz, S.: Energy-utility quantiles. In: Rozier, K.Y. (ed.) NFM 2014. LNCS, vol. 8430, pp. 285–299. Springer, Heidelberg (2014)Google Scholar
  5. 5.
    Baier, C., Daum, M., Engel, B., Härtig, H., Klein, J., Klüppelholz, S., Märcker, S., Tews, H., Völp, M.: Chiefly symmetric: Results on the scalability of probabilistic model checking for operating-system code. In: 7th Conference on Systems Software Verification (SSV). Electronic Proceedings in Theoretical Computer Science, vol. 102, pp. 156–166 (2012)Google Scholar
  6. 6.
    Baier, C., Daum, M., Engel, B., Härtig, H., Klein, J., Klüppelholz, S., Märcker, S., Tews, H., Völp, M.: Waiting for locks: How long does it usually take? In: Stoelinga, M., Pinger, R. (eds.) FMICS 2012. LNCS, vol. 7437, pp. 47–62. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Baier, C., Engel, B., Klüppelholz, S., Märcker, S., Tews, H., Völp, M.: A probabilistic quantitative analysis of probabilistic-write/copy-select. In: Brat, G., Rungta, N., Venet, A. (eds.) NFM 2013. LNCS, vol. 7871, pp. 307–321. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  8. 8.
    Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press (2008)Google Scholar
  9. 9.
    Baier, C., Klein, J., Klüppelholz, S., Märcker, S.: Computing conditional probabilities in Markovian models efficiently. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 515–530. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  10. 10.
    Barnat, J., Brim, L., Černá, I., Češka, M., Tůmová, J.: ProbDiVinE-MC: Multi-core LTL model checker for probabilistic systems. In: 5th International Conference on Quantitative Evaluation of Systems (QEST), pp. 77–78. IEEE Computer Society (2008)Google Scholar
  11. 11.
    Bianco, A., de Alfaro, L.: Model checking of probabilistic and non-deterministic systems. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 499–513. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  12. 12.
    Boker, U., Chatterjee, K., Henzinger, T., Kupferman, O.: Temporal specifications with accumulative values. In: 26th Annual IEEE Symposium on Logic in Computer Science (LICS), pp. 43–52. IEEE Computer Society (2011)Google Scholar
  13. 13.
    Brázdil, T., Brozek, V., Etessami, K.: One-counter stochastic games. In: 30th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS). Leibniz International Proceedings in Informatics (LIPIcs), vol. 8, pp. 108–119. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2010)Google Scholar
  14. 14.
    Brázdil, T., Brozek, V., Etessami, K., Kucera, A.: Approximating the termination value of one-counter MDPs and stochastic games. Information and Computation 222, 121–138 (2013)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Brázdil, T., Kučera, A., Stražovský, O.: On the Decidability of Temporal Properties of Probabilistic Pushdown Automata. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 145–157. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Chatterjee, K., Doyen, L.: Energy and mean-payoff parity Markov decision processes. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 206–218. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  17. 17.
    Chatterjee, K., Doyen, L.: Energy parity games. Theoretical Computer Science 458, 49–60 (2012)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Chatterjee, K., Majumdar, R., Henzinger, T.: Markov decision processes with multiple objectives. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 325–336. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Chen, T., Han, T., Katoen, J.-P., Mereacre, A.: Model checking of continuous-time Markov chains against timed automata specifications. Logical Methods in Computer Science 7(1) (2011)Google Scholar
  20. 20.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press (2000)Google Scholar
  21. 21.
    Desharnais, J., Panangaden, P.: Continuous stochastic logic characterizes bisimulation of continuous-time Markov processes. Journal of Logic and Algebraic Programming 56(1-2), 99–115 (2003)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Dubslaff, C., Klüppelholz, S., Baier, C.: Probabilistic model checking for energy analysis in software product lines. In: 13th International Conference on Modularity, MODULARITY 2014 ( to appear, 2014) Google Scholar
  23. 23.
    Etessami, K., Kwiatkowska, M., Vardi, M., Yannakakis, M.: Multi-objective model checking of Markov decision processes. Logical Methods in Computer Science 4(4) (2008)Google Scholar
  24. 24.
    Forejt, V., Kwiatkowska, M., Norman, G., Parker, D., Qu, H.: Quantitative multi-objective verification for probabilistic systems. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 112–127. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  25. 25.
    Gao, Y., Xu, M., Zhan, N., Zhang, L.: Model checking conditional CSL for continuous-time Markov chains. Information Processing Letters 113(1-2), 44–50 (2013)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Garavel, H., Lang, F., Mateescu, R., Serwe, W.: CADP 2011: a toolbox for the construction and analysis of distributed processes. Software Tools and Technology Transfer (STTT) 15(2), 89–107 (2013)CrossRefMATHGoogle Scholar
  27. 27.
    Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)MATHGoogle Scholar
  28. 28.
    Haverkort, B.: Performance of Computer Communication Systems: A Model-Based Approach. Wiley (1998)Google Scholar
  29. 29.
    Ji, M., Wu, D., Chen, Z.: Verification method of conditional probability based on automaton. Journal of Networks 8(6), 1329–1335 (2013)CrossRefGoogle Scholar
  30. 30.
    Katoen, J.-P., Zapreev, I., Hahn, E., Hermanns, H., Jansen, D.: The ins and outs of the probabilistic model checker MRMC. Performance Evaluation 68(2), 90–104 (2011)CrossRefGoogle Scholar
  31. 31.
    Kulkarni, V.: Modeling and Analysis of Stochastic Systems. Chapman & Hall (1995)Google Scholar
  32. 32.
    Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic symbolic model checking with PRISM: A hybrid approach. International Journal on Software Tools for Technology Transfer (STTT) 6(2), 128–142 (2004)CrossRefMATHGoogle Scholar
  33. 33.
    Laroussinie, F., Sproston, J.: Model checking durational probabilistic systems. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 140–154. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  34. 34.
    McGuire, N.: Probabilistic write copy select. In: 13th Real-Time Linux Workshop, pp. 195–206 (2011)Google Scholar
  35. 35.
    Oualhadj, Y.: The value problem in stochastic games. PhD thesis, Université Science et Technologies, Bordeaux I (2012)Google Scholar
  36. 36.
    Panangaden, P.: Measure and probability for concurrency theorists. Theoretical Computer Science 253(2), 287–309 (2001)MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Perny, P., Weng, P.: On finding compromise solutions in multiobjective Markov decision processes. In: 19th European Conference on Artificial Intelligence (ECAI). Frontiers in Artificial Intelligence and Applications, vol. 215, pp. 969–970. IOS Press (2010)Google Scholar
  38. 38.
    Puterman, M.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons, Inc., New York (1994)Google Scholar
  39. 39.
    Stewart, A., Etessami, K., Yannakakis, M.: Upper bounds for newton’s method on monotone polynomial systems, and P-time model checking of probabilistic one-counter automata. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 495–510. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  40. 40.
    Ummels, M., Baier, C.: Computing quantiles in Markov reward models. In: Pfenning, F. (ed.) FOSSACS 2013. LNCS, vol. 7794, pp. 353–368. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  41. 41.
    Vardi, M.: Automatic verification of probabilistic concurrent finite-state programs. In: 26th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 327–338. IEEE Computer Society (1985)Google Scholar
  42. 42.
    Viswanathan, B., Aggarwal, V., Nair, K.: Multiple criteria Markov decision processes. TIMS Studies in the Management Sciences 6, 263–272 (1977)Google Scholar
  43. 43.
    von Essen, C., Jobstmann, B.: Synthesizing efficient controllers. In: Kuncak, V., Rybalchenko, A. (eds.) VMCAI 2012. LNCS, vol. 7148, pp. 428–444. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Christel Baier
    • 1
  • Clemens Dubslaff
    • 1
  • Joachim Klein
    • 1
  • Sascha Klüppelholz
    • 1
  • Sascha Wunderlich
    • 1
  1. 1.Institute for Theoretical Computer ScienceTechnische Universität DresdenGermany

Personalised recommendations