Importance sampling for the simulation of highly reliable Markovian systems
Management Science
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
UPPAAL—a tool suite for automatic verification of real-time systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Guarded commands, nondeterminacy and formal derivation of programs
Communications of the ACM
Proceedings of the 32nd conference on Winter simulation
PRISM: Probabilistic Symbolic Model Checker
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
Probabilistic Verification of Discrete Event Systems Using Acceptance Sampling
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
VESTA: A Statistical Model-checker and Analyzer for Probabilistic Systems
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
A Bayesian Approach to Model Checking Biological Systems
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Rare Event Simulation using Monte Carlo Methods
Rare Event Simulation using Monte Carlo Methods
Statistical model checking for cyber-physical systems
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Ymer: a statistical model checker
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Statistical abstraction and model-checking of large heterogeneous systems
FMOODS'10/FORTE'10 Proceedings of the 12th IFIP WG 6.1 international conference and 30th IFIP WG 6.1 international conference on Formal Techniques for Distributed Systems
Coupling and importance sampling for statistical model checking
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
A platform for high performance statistical model checking --- PLASMA
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy
IEEE Transactions on Information Theory
Statistical model checking qos properties of systems with SBIP
ISoLA'12 Proceedings of the 5th international conference on Leveraging Applications of Formal Methods, Verification and Validation: technologies for mastering change - Volume Part I
Runtime verification of biological systems
ISoLA'12 Proceedings of the 5th international conference on Leveraging Applications of Formal Methods, Verification and Validation: technologies for mastering change - Volume Part I
Importance splitting for statistical model checking rare properties
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Automated rare event simulation for stochastic petri nets
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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Statistical model checking avoids the exponential growth of states associated with probabilistic model checking by estimating probabilities from multiple executions of a system and by giving results within confidence bounds. Rare properties are often important but pose a particular challenge for simulation-based approaches, hence a key objective for statistical model checking (SMC) is to reduce the number and length of simulations necessary to produce a result with a given level of confidence. Importance sampling can achieves this, however to maintain the advantages of SMC it is necessary to find good importance sampling distributions without considering the entire state space. Here we present a simple algorithm that uses the notion of cross-entropy to find an optimal importance sampling distribution. In contrast to previous work, our algorithm uses a naturally defined low dimensional vector of parameters to specify this distribution and thus avoids the intractable explicit representation of a transition matrix. We show that our parametrisation leads to a unique optimum and can produce many orders of magnitude improvement in simulation efficiency. We demonstrate the efficacy of our methodology by applying it to models from reliability engineering and biochemistry.