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VESTA: A Statistical Model-checker and Analyzer for Probabilistic Systems

VESTA is a tool for statistical model checking and analysis of probabilistic systems, supporting various quantitative queries. Download it at http://osl.cs.uiuc.edu/~ksen/vesta2/

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VESTA: A Statistical Model-checker and Analyzer for Probabilistic Systems

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  1. VESTA: A Statistical Model-checker and Analyzer for Probabilistic Systems Authors: Koushik Sen Mahesh Viswanathan Gul Agha University of Illinois at Urbana-Champaign YoungMin Kwon

  2. Vesta Tool • Input: A probabilistic model M given as • a Java class on which one can perform discrete-event simulation • a CTMC model in a special language (similar to that used in PRISM) • a Probabilistic Rewrite Theory in Maude

  3. Vesta Tool • Input: A probabilistic model M given as • a Java class on which one can perform discrete-event simulation • a CTMC model in a special language (similar to that used in PRISM) • a Probabilistic Rewrite Theory in Maude • Input: A formula F in Continuous Stochastic Logic (CSL) or Probabilistic Computation Tree Logic (PCTL) • Vesta can model check F against M, i.e. check if M ² F

  4. Vesta Tool • Input: A probabilistic model M given as • a Java class on which one can perform discrete-event simulation • a CTMC model in a special language (similar to that used in PRISM) • a Probabilistic Rewrite Theory in Maude • Input: A formula F in Continuous Stochastic Logic (CSL) or Probabilistic Computation Tree Logic (PCTL) • Vesta can model check F against M, i.e. check if M ² F • Input: An expression E in Quantitative Temporal Expressions (QuaTEx) • Vesta can compute the expected value of E

  5. Model Assumption • Sample execution paths can be generated through discrete-event simulation • Execution paths are sequences of the form = s0! s1! s2! … where each si is a state of the model and ti2R>0 is the time spent in the state si before moving to the state si+1 • A probability space can be defined on the execution paths of the model in such a way that the paths satisfying any path formula in our concerned logic (CSL or PCTL), is measurable t0 t1 t2

  6. Continuous Stochastic Logic (CSL) and PCTL •  ::= true | a | Æ | : | PQ p() •  ::=  U<t |  U  | X  where Q2 {<,>,¸,·} • P< 0.5(§full) • Probability that queue becomes full is less than 0.5 • P>0.98(: retransmit U receive) • Probability that a message is eventually received successfully without any need for retransmission is greater than 0.98

  7. Model Checking: Main Result Summarized • Our algorithm A takes as input • a stochastic model M, • a formulain CSL, • error bounds  and, and • three other parameters 1, 2, and ps. • The result of model checking is denoted by A1,2,ps(M, ,,) • can be either true or false. • Details in [Sen et al. CAV’05]

  8. Model Checking: Main Result Summarized Theorem: If the model M satisfies the following conditions • C1: For every subformula of the form P¸ p in the formula  and for every state s in M, the probability that a path from s satisfies  must not lie in the range [ (p-1-)/(1-),(p+1)/(1-)] • C2: For any subformula of the form 1 U 2 and for every state s in M, the probability that a path from s satisfies 1 U 2 must not lie in the range (0, 2/((1-ps)N-1qN-1)], where N is the number of states in the model M and q is the smallest non-zero transition probability in M • Then the algorithm provides the following guarantees • R1 : • Pr[A1,2,ps(M, ,,) = true | M 2] · • Pr[A1,2,ps(M, ,,) = false | M²] ·

  9. Quantitative Queries Using QuaTEx • What is the expected number of clients that successfully connect to S? CountConnected() = if completed() then count() else ° (CountConnected()) fi; eval E[CountConnected()]

  10. Quantitative Queries Using QuaTEx • What is the probability that a client connected to S within 10 seconds after it initiated the connection request? Prob() = if globaltime()>10 then 0.0 else if connected() then 1.0 else ° (Prob()) fi fi; eval E[Prob()]

  11. Evaluation of QuaTEx • The expected value of a QuaTEx expression is statistically evaluated with respect to two parameters  and  provided as input. • We approximate the expected value by the mean of n samples such that the size of (1−)100% confidence interval for the expected value computed from the samples is bounded by. • Details in [Agha et al. QAPL’05]

  12. Vesta Screenshot

  13. Conclusion • Vesta 2.0 supports • statistical model checking of probabilistic systems • query various quantitative aspects of a probabilistic system • The tool is available for download at http://osl.cs.uiuc.edu/~ksen/vesta2/

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