Safe On-The-Fly Steady-State Detection for Time-Bounded Reachability

The time-bounded reachability problem for continuous-time Markov chains (CTMCs) amounts to determine the probability to reach a (set of) goal state(s) within a given time span, such that prior to reaching the goal certain states are avoided. Efficient algorithms for time-bounded reachability are at the heart of probabilistic model checkers such as PRISM and ETMCC. For large time spans, on-the-fly steady-state detection is commonly applied. To obtain correct results (up to a given accuracy), it is essential to avoid detecting premature stationarity. This paper gives a detailed account of criteria for steady-state detection in the setting of time-bounded reachability. This is done for forward and backward reachability algorithms. As a spin-off of this study, new results for on-the-fly steady-state detection during CTMC transient analysis are reported. Based on these results, a precise procedure for steady-state detection for time-bounded reachability is obtained. Experiments show the impact of these results in probabilistic model checking

[1]  Håkan L. S. Younes,et al.  Numerical vs. Statistical Probabilistic Model Checking: An Empirical Study , 2004, TACAS.

[2]  Peter W. Glynn,et al.  Computing Poisson probabilities , 1988, CACM.

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

[4]  Joost-Pieter Katoen,et al.  A Markov reward model checker , 2005, Second International Conference on the Quantitative Evaluation of Systems (QEST'05).

[5]  H. Tijms.  A First Course in Stochastic Models , 2003 .

[6]  Robert K. Brayton,et al.  Model-checking continuous-time Markov chains , 2000, TOCL.

[7]  Kishor S. Trivedi,et al.  STIFFNESS-TOLERANT METHODS FOR TRANSIENT ANALYSIS OF STIFF MARKOV CHAINS , 1994 .

[8]  Bruno Sericola.  Availability Analysis of Repairable Computer Systems and Stationarity Detection , 1999, IEEE Trans. Computers.

[9]  Holger Hermanns,et al.  A tool for model-checking Markov chains , 2003, International Journal on Software Tools for Technology Transfer.

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

[11]  Mahesh Viswanathan,et al.  On Statistical Model Checking of Stochastic Systems , 2005, CAV.

[12]  Marta Z. Kwiatkowska,et al.  Model checking for probability and time: from theory to practice , 2003, 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings..

[13]  Håkan L. S. Younes,et al.  Numerical vs. statistical probabilistic model checking , 2006, International Journal on Software Tools for Technology Transfer.

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

[15]  Susanna Donatelli,et al.  CSL Model Checking for the GreatSPN Tool , 2004, ISCIS.

[16]  Marta Z. Kwiatkowska,et al.  PRISM 2.0: a tool for probabilistic model checking , 2004, First International Conference on the Quantitative Evaluation of Systems, 2004. QEST 2004. Proceedings..

[17]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

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

[19]  Diego Latella,et al.  Model checking dependability attributes of wireless group communication , 2004, International Conference on Dependable Systems and Networks, 2004.

[20]  Henk C. Tijms,et al.  A First Course in Stochastic Models: Tijms/Stochastic Models , 2003 .

[21]  William J. Stewart,et al.  A comparison of numerical techniques in Markov modeling , 1978, CACM.

[22]  Håkan L. S. Younes.  Ymer: A Statistical Model Checker , 2005, CAV.

[23]  Marta Z. Kwiatkowska,et al.  PRISM: Probabilistic Symbolic Model Checker , 2002, Computer Performance Evaluation / TOOLS.

[24]  Christel Baier,et al.  Model-Checking Algorithms for , 2003 .

[25]  Joost-Pieter Katoen,et al.  Model-checking large structured Markov chains , 2003, J. Log. Algebraic Methods Program..

[26]  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.

[27]  Christel Baier,et al.  Model-Checking Algorithms for Continuous-Time Markov Chains , 2002, IEEE Trans. Software Eng..

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