Analysis of restart simulation: Theoretical basis and sensitivity study

RESTART (Repetitive Simulation Trials After Reaching Thresholds) is a widely applicable accelerated simulation technique that allows the evaluation of extremely low probabilities. This paper revisits the theoretical basis of RESTART in a more general and rigorous way. The unbiasedness of the estimator is proved and its variance is derived without need of making any assumption on the simulated system. From this analysis, the gain obtained with RESTART as well as the optimal parameter values that maximise the gain are derived. The sensitivity of the method to the choice of the importance function, threshold values and number of retrials for each threshold is studied, providing simple bounds on me impact on the gain of each of these choices.