Conditional Monte Carlo With Intermediate Estimations for Simulation of Markovian Systems

For systems that are suitable to be modelled by continuous Markov chains, dependability analysis is not always straightforward. When such systems are large and complex, it is usually impossible to compute their dependability measures exactly. An alternative solution is to estimate them by simulation, typically by Monte Carlo simulation. But for highly reliable systems standard simulation can not reach satisfactory accuracy levels (measured by the variance of the estimator) within reasonable computing times. Conditional Monte Carlo with Intermediate Estimations (CMIE) is a simulation method proposal aimed at making accurate estimations of dependability measures on highly reliable Markovian systems. The basis of CMIE is introduced, the unbiasedness of the corresponding estimator is proven, and its variance is shown to be lower than the variance of the standard estimator. A variant of the basic scheme, that applies to large and highly reliable multicomponent systems, is introduced. Some experimental results are shown. Keywords—dependability, simulation, rare event, Conditional Monte Carlo.