A Markov Chain Model Checker

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 and the continuous time setting. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker (E ⊢ MC2), 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 ⊢ MC2.

[1]  Moshe Y. Vardi.  Automatic verification of probabilistic concurrent finite state programs , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[2]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[3]  Ignas G. Niemegeers,et al.  Performability Modelling Tools and Techniques , 1996, Perform. Evaluation.

[4]  Holger Hermanns,et al.  Compositional performance modelling with the TIPPtool , 2000, Perform. Evaluation.

[5]  William H. Sanders,et al.  An Efficient Disk-Based Tool for Solving Very Large Markov Models , 1997, Computer Performance Evaluation.

[6]  Joost-Pieter Katoen,et al.  Towards Model Checking Stochastic Process Algebra , 2000, IFM.

[7]  Luca de Alfaro,et al.  Symbolic Model Checking of Probabilistic Processes Using MTBDDs and the Kronecker Representation , 2000, TACAS.

[8]  Holger Hermanns.  Performance and reliability model checking and model construction , 2000 .

[9]  Brigitte Plateau,et al.  Stochastic Automata Network For Modeling Parallel Systems , 1991, IEEE Trans. Software Eng..

[10]  Christel Baier,et al.  Approximate Symbolic Model Checking of Continuous-Time Markov Chains , 1999, CONCUR.

[11]  Ivan Christoff,et al.  Reasonong about Safety and Liveness Properties for Probabilistic Processes , 1992, FSTTCS.

[12]  Marco Ajmone Marsan,et al.  A class of generalised stochastic petri nets for the performance evaluation of multiprocessor systems , 1983, SIGMETRICS '83.

[13]  M. Siegle,et al.  Multi Terminal Binary Decision Diagrams to Represent and Analyse Continuous Time Markov Chains , 1999 .

[14]  Joost-Pieter Katoen,et al.  Process algebra for performance evaluation , 2002, Theor. Comput. Sci..

[15]  Mihalis Yannakakis,et al.  Verifying temporal properties of finite-state probabilistic programs , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[16]  Joost-Pieter Katoen,et al.  On the use of model checking techniques for dependability evaluation , 2000, Proceedings 19th IEEE Symposium on Reliable Distributed Systems SRDS-2000.

[17]  Adnan Aziz,et al.  It Usually Works: The Temporal Logic of Stochastic Systems , 1995, CAV.

[18]  Christel Baier,et al.  Symbolic Model Checking for Probabilistic Processes , 1997, ICALP.

[19]  Sérgio Vale Aguiar Campos,et al.  ProbVerus: Probabilistic Symbolic Model Checking , 1999, ARTS.

[20]  Boudewijn R. Haverkort,et al.  Performance of computer communication systems - a model-based approach , 1998 .

[21]  Nicolas D. Georganas,et al.  Queueing networks - exact computational algorithms: a unified theory based on decomposition and aggregation , 1989, Computer systems.

[22]  Joost-Pieter Katoen,et al.  Faster and Symbolic CTMC Model Checking , 2001, PAPM-PROBMIV.

[23]  William H. Sanders,et al.  An Efficient Disk-Based Tool for Solving Large Markov Models , 1998, Perform. Evaluation.

[24]  Marco Ajmone Marsan,et al.  A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems , 1984, TOCS.

[25]  Christel Baier,et al.  Model Checking Continuous-Time Markov Chains by Transient Analysis , 2000, CAV.

[26]  Christel Baier,et al.  On the Verification of Qualitative Properties of Probabilistic Processes under Fairness Constraints , 1998, Inf. Process. Lett..

[27]  William J. Stewart,et al.  Introduction to the numerical solution of Markov Chains , 1994 .

[28]  Robert K. Brayton,et al.  Verifying Continuous Time Markov Chains , 1996, CAV.

[29]  Enrico Macii,et al.  Markovian analysis of large finite state machines , 1996, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[30]  Jane Hillston,et al.  A compositional approach to performance modelling , 1996 .

[31]  Joost-Pieter Katoen,et al.  Implementing a Model Checker for Performability Behaviour , 2001 .

[32]  Lars ke Fredlund.  The Timing and Probability Workbench: A Tool for Analysing Timed Processes , 1994 .

[33]  Kishor S. Trivedi,et al.  Stochastic Petri Net Models of Polling Systems , 1990, IEEE J. Sel. Areas Commun..