Rare event RESTART simulation of two-stage networks

REpetitive Simulation Trials After Reaching Thresholds (RESTART) is a widely applied accelerated simulation technique that allows the evaluation of extremely low probabilities. In this method a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of the rare event is higher. Formulas for evaluating the optimal number of regions and retrials as well as guidelines for obtaining suitable importance functions were provided in previous papers. Nevertheless, further investigations are required to apply these guidelines to practical cases.In this paper, we obtain efficient importance functions for networks with two stages and different nodes in each stage. Some approximations are used to derive the formulas. The goodness of such approximations is supported by the simulation results obtained. The methodology applied can be extended to other networks.