A comparison of restart implementations

The RESTART method is a widely applicable simulation technique for the estimation of rare event probabilities. The method is based on the idea to restart the simulation in certain system states, in order to generate more occurrences of the rare event. One of the main questions for any RESTART implementation is how and when to restart the simulation, in order to achieve the most accurate results for a fixed simulation effort. In this paper we investigate and compare, both theoretically and empirically, different implementations of the RESTART method. We find that the original RESTART implementation, in which each path is split into a fixed number of copies, may not be the most efficient one. It is generally better to fix the total simulation effort for each stage of the simulation. Furthermore, given this effort, the best strategy is to restart an equal number of times from each state, rather than to restart each time from a randomly chosen state.