Numerical transient analysis of Markov models
Computers and Operations Research
A Unified Framework for Simulating Markovian Models of Highly Dependable Systems
IEEE Transactions on Computers
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Importance sampling for the simulation of highly reliable Markovian systems
Management Science
The balanced likelihood ratio method for estimating performance measures of highly reliable systems
Proceedings of the 30th conference on Winter simulation
Variance reduction in mean time to failure simulations
WSC '88 Proceedings of the 20th conference on Winter simulation
Measure specific dynamic importance sampling for availability simulations
WSC '87 Proceedings of the 19th conference on Winter simulation
Simulation and analysis of highly reliable systems
Simulation and analysis of highly reliable systems
Fast Simulation of Markov Chains with Small Transition Probabilities
Management Science
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This paper targets the simulation of continuous-time Markov chain models of fault-tolerant systems with deferred repair. We start by stating sufficient conditions for a given importance sampling scheme to satisfy the bounded relative error property. Using those sufficient conditions, it is noted that many previously proposed importance sampling techniques such as failure biasing and balanced failure biasing satisfy that property. Then, we adapt the importance sampling schemes failure transition distance biasing and balanced failure transition distance biasing so as to develop new importance sampling schemes which can be implemented with moderate effort and at the same time can be proved to be more efficient for balanced systems than the simpler failure biasing and balanced failure biasing schemes. The increased efficiency for both balanced and unbalanced systems of the new adapted importance sampling schemes is illustrated using examples.