Skip to main content

Probabilistic Model Checking for Energy-Utility Analysis

  • Chapter
Horizons of the Mind. A Tribute to Prakash Panangaden

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8464))

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.

This work was partly funded by the DFG through the CRC 912 HAEC, the cluster of excellence cfAED, the project QuaOS, the Graduiertenkolleg 1763 (QuantLA), and the DFG/NWO-project ROCKS and partially by Deutsche Telekom Stiftung, the ESF young researcher groups IMData 100098198 and SREX 100111037, and the EU-FP-7 grant 295261 (MEALS).

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. Andrés, M.: Quantitative Analysis of Information Leakage in Probabilistic and Nondeterministic Systems. PhD thesis, UB Nijmegen (2011)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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. 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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  8. Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press (2008)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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. 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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  17. Chatterjee, K., Doyen, L.: Energy parity games. Theoretical Computer Science 458, 49–60 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press (2000)

    Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  27. Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  28. Haverkort, B.: Performance of Computer Communication Systems: A Model-Based Approach. Wiley (1998)

    Google Scholar 

  29. Ji, M., Wu, D., Chen, Z.: Verification method of conditional probability based on automaton. Journal of Networks 8(6), 1329–1335 (2013)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  31. Kulkarni, V.: Modeling and Analysis of Stochastic Systems. Chapman & Hall (1995)

    Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  34. McGuire, N.: Probabilistic write copy select. In: 13th Real-Time Linux Workshop, pp. 195–206 (2011)

    Google Scholar 

  35. Oualhadj, Y.: The value problem in stochastic games. PhD thesis, Université Science et Technologies, Bordeaux I (2012)

    Google Scholar 

  36. Panangaden, P.: Measure and probability for concurrency theorists. Theoretical Computer Science 253(2), 287–309 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  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. Puterman, M.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons, Inc., New York (1994)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Viswanathan, B., Aggarwal, V., Nair, K.: Multiple criteria Markov decision processes. TIMS Studies in the Management Sciences 6, 263–272 (1977)

    Google Scholar 

  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)

    Chapter  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 International Publishing Switzerland

About this chapter

Cite this chapter

Baier, C., Dubslaff, C., Klein, J., Klüppelholz, S., Wunderlich, S. (2014). Probabilistic Model Checking for Energy-Utility Analysis. In: van Breugel, F., Kashefi, E., Palamidessi, C., Rutten, J. (eds) Horizons of the Mind. A Tribute to Prakash Panangaden. Lecture Notes in Computer Science, vol 8464. Springer, Cham. https://doi.org/10.1007/978-3-319-06880-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-06880-0_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06879-4

  • Online ISBN: 978-3-319-06880-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics