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A Markov Chain Model Checker

  • Holger Hermanns
  • Joost-Pieter Katoen
  • Joachim Meyer-Kayser
  • Markus Siegle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1785)

Abstract

Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17,6] and the continuous time setting [4,8]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker (E ⊢ MC 2), where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore we report on first successful applications of the tool to non-trivial examples, highlighting lessons learned during development and application of E ⊢ MC 2.

Keywords

Markov Chain Model Checker Temporal Logic Polling System Interpolation Point 
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.

References

  1. 1.
    M. Ajmone Marsan, G. Conte, and G. Balbo. A class of generalised stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Tr. on Comp. Sys., 2(2): 93–122, 1984. 348, 358CrossRefGoogle Scholar
  2. 2.
    L. de Alfaro, M.Z. Kwiatkowska, G. Norman, D. Parker and R. Segala. Symbolic model checking for probabilistic processes using MTBDDs and the Kronecker representation. In TACAS, LNCS (this volume), 2000. 349Google Scholar
  3. 3.
    A. Aziz, V. Singhal, F. Balarin, R. Brayton and A. Sangiovanni-Vincentelli. It usually works: the temporal logic of stochastic systems. In CAV, LNCS 939: 155–165, 1995. 347Google Scholar
  4. 4.
    A. Aziz, K. Sanwal, V. Singhal and R. Brayton. Verifying continuous time Markov chains. In CAV, LNCS 1102: 269–276, 1996. 347, 348Google Scholar
  5. 5.
    C. Baier. On algorithmic verification methods for probabilistic systems. Habilitation thesis, Univ. of Mannheim, 1999. 347, 352Google Scholar
  6. 6.
    C. Baier, E. Clarke, V. Hartonas-Garmhausen, M. Kwiatkowska, and M. Ryan. Symbolic model checking for probabilistic processes. In ICALP, LNCS 1256: 430–440, 1997. 347Google Scholar
  7. 7.
    C. Baier, B.R. Haverkort, H. Hermanns and J.-P. Katoen. Model checking continuous-time Markov chains by transient analysis. 2000 (submitted). 360Google Scholar
  8. 8.
    C. Baier, J.-P. Katoen and H. Hermanns. Approximate symbolic model checking of continuous-time Markov chains. In CONCUR, LNCS 1664: 146–162, 1999. 347, 348, 349, 350, 351, 352, 360Google Scholar
  9. 9.
    C. Baier and M. Kwiatkowska. On the verification of qualitative properties of probabilistic processes under fairness constraints. Inf. Proc. Letters, 66(2): 71–79, 1998. 350, 353zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    I. Christoff and L. Christoff. Reasoning about safety and liveness properties for probabilistic systems. In FSTTCS, LNCS 652: 342–355, 1992. 347Google Scholar
  11. 11.
    E.M. Clarke, E.A. Emerson and A.P. Sistla. Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Tr. on Progr. Lang. and Sys., 8(2): 244–263, 1986. 350, 351zbMATHCrossRefGoogle Scholar
  12. 12.
    A.E. Conway and N.D. Georganas. Queueing Networks — Exact Computational Algorithms. MIT Press, 1989. 348, 355Google Scholar
  13. 13.
    C. Courcoubetis and M. Yannakakis. Verifying temporal properties of finite-state probabilistic programs. In Proc. IEEE Symp. on Found. of Comp. Sci., pp. 338–345, 1988. 347, 352Google Scholar
  14. 14.
    D.D. Deavours and W.H. Sanders. An efficient disk-based tool for solving very large Markov models. In Comp. Perf. Ev., LNCS 1245: 58–71, 1997. 352Google Scholar
  15. 15.
    L. Fredlund. The timing and probability workbench: a tool for analysing timed processes. Tech. Rep. No. 49, Uppsala Univ., 1994. 348Google Scholar
  16. 16.
    G. Hachtel, E. Macii, A. Padro and F. Somenzi. Markovian analysis of large finite-state machines. IEEE Tr. on CAD of Integr. Circ. and Sys., 15(12): 1479–1493, 1996. 360CrossRefGoogle Scholar
  17. 17.
    H. Hansson and B. Jonsson. A logic for reasoning about time and reliability. Form. Asp. of Comp., 6(5): 512–535, 1994. 347, 348, 352, 353, 360zbMATHCrossRefGoogle Scholar
  18. 18.
    V. Hartonas-Garmhausen, S. Campos and E.M. Clarke. ProbVerus: probabilistic symbolic model checking. In ARTS, LNCS 1601: 96–111, 1999. 348Google Scholar
  19. 19.
    B.R. Haverkort. Performance of Computer Communication Systems: A Model-Based Approach. John Wiley & Sons, 1998. 351Google Scholar
  20. 20.
    B.R. Haverkort and I.G. Niemegeers. Performability modelling tools and techniques. Perf. Ev., 25: 17–40, 1996. 350zbMATHCrossRefGoogle Scholar
  21. 21.
    H. Hermanns, U. Herzog and J.-P. Katoen. Process algebra for performance evaluation. Th. Comp. Sci., 2000 (to appear). 348Google Scholar
  22. 22.
    H. Hermanns, U. Herzog, U. Klehmet, V. Mertsiotakis and M. Siegle. Compositional performance modelling with the TIPPtool. Perf. Ev., 39(1–4): 5–35, 2000. 351, 359zbMATHCrossRefGoogle Scholar
  23. 23.
    H. Hermanns, J. Meyer-Kayser and M. Siegle. Multi-terminal binary decision diagrams to represent and analyse continuous-time Markov chains. In Proc. 3rd Int. Workshop on the Num. Sol. of Markov Chains, pp. 188–207, 1999. 355, 356, 360Google Scholar
  24. 24.
    J. Hillston. A Compositional Approach to Performance Modelling. Cambridge University Press, 1996. 348Google Scholar
  25. 25.
    O.C. Ibe and K.S. Trivedi. Stochastic Petri net models of polling systems. IEEE J. on Sel. Areas in Comms., 8(9): 1649–1657, 1990. 358CrossRefGoogle Scholar
  26. 26.
    B. Plateau and K. Atif, Stochastic automata networks for modeling parallel systems. IEEE Tr. on Softw. Eng., 17(10): 1093–1108, 1991. 348CrossRefMathSciNetGoogle Scholar
  27. 27.
    W. Stewart. Introduction to the Numerical Solution of Markov Chains. Princeton Univ. Press, 1994. 348, 349, 350, 351, 355Google Scholar
  28. 28.
    R.E. Tarjan. Depth-first search and linear graph algorithms. SIAM J. of Comp., 1: 146–160, 1972. 351zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    M.Y. Vardi. Automatic verification of probabilistic concurrent finite state programs. In Proc. IEEE Symp. on Found. of Comp. Sci., pp. 327–338, 1985. 347Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Holger Hermanns
    • 1
  • Joost-Pieter Katoen
    • 1
  • Joachim Meyer-Kayser
    • 2
  • Markus Siegle
    • 2
  1. 1.Formal Methods and Tools GroupUniversity of TwenteEnschedeThe Netherlands
  2. 2.Lehrstuhl für Informatik 7University of Erlangen-NürnbergErlangenGermany

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