On the efficiency of RESTART for multidimensional state systems

RESTART (Repetitive Simulation Trials After Reaching Thresholds) is a widely applicable accelerated simulation technique that allows the evaluation of extremely low probabilities. The focus of this article is on providing guidelines for achieving a high efficiency in a simulation with RESTART. Emphasis is placed on the choice of the importance function, that is, the function of the system state for determining when retrials are made. A heuristic approach which is shown to be effective for some systems is proposed for this choice. A two-queue tandem network is used to illustrate the efficiency achieved following these guidelines. The importance function chosen in this example shows that an appropriate choice of the importance function leads to an efficient simulation of a system with multidimensional state space. Also presented are sufficient conditions for achieving asymptotic efficiency, and it is shown that they are not very restrictive in RESTART simulation.