A Unified Framework for Simulating Markovian Models of Highly Dependable Systems
IEEE Transactions on Computers
Fast Simulation of Highly Dependable Systems with General Failure and Repair Processes
IEEE Transactions on Computers
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)
Performance of Computer Communication Systems: A Model-Based Approach
Performance of Computer Communication Systems: A Model-Based Approach
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Verifying Continuous Time Markov Chains
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Probabilistic Verification of Discrete Event Systems Using Acceptance Sampling
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Fast Simulation of Markov Chains with Small Transition Probabilities
Management Science
Probability in the Engineering and Informational Sciences
Numerical vs. statistical probabilistic model checking
International Journal on Software Tools for Technology Transfer (STTT)
Estimating the probability of a rare event over a finite time horizon
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Arcade - A Formal, Extensible, Model-Based Dependability Evaluation Framework
ICECCS '08 Proceedings of the 13th IEEE International Conference on on Engineering of Complex Computer Systems
Rare Event Simulation for Highly Dependable Systems with Fast Repairs
QEST '10 Proceedings of the 2010 Seventh International Conference on the Quantitative Evaluation of Systems
Importance splitting for statistical model checking rare properties
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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Probabilistic model checking has been used recently to assess, among others, dependability measures for a variety of systems. However, the numerical methods employed, such as those supported by model checking tools such as PRISM and MRMC, suffer from the state-space explosion problem. The main alternative is statistical model checking, which uses standard Monte Carlo simulation, but this performs poorly when small probabilities need to be estimated. Therefore, we propose a method based on importance sampling to speed up the simulation process in cases where the failure probabilities are small due to the high speed of the system's repair units. This setting arises naturally in Markovian models of highly dependable systems. We show that our method compares favourably to standard simulation, to existing importance sampling techniques, and to the numerical techniques of PRISM.