Green Simulation with Database Monte Carlo

In a setting in which experiments are performed repeatedly with the same simulation model, green simulation means reusing outputs from previous experiments to answer the question currently being asked of the model. In this article, we address the setting in which experiments are run to answer questions quickly, with a time limit providing a fixed computational budget, and then idle time is available for further experimentation before the next question is asked. The general strategy is database Monte Carlo for green simulation: the output of experiments is stored in a database and used to improve the computational efficiency of future experiments. In this article, the database provides a quasi-control variate, which reduces the variance of the estimated mean response in a future experiment that has a fixed computational budget. We propose a particular green simulation procedure using quasi-control variates, addressing practical issues such as experiment design, and analyze its theoretical properties. We show that, under some conditions, the variance of the estimated mean response in an experiment with a fixed computational budget drops to zero over a sequence of repeated experiments, as more and more idle time is invested in creating databases. Our numerical experiments on the procedure show that using idle time to create databases of simulation output provides variance reduction immediately, and that the variance reduction grows over time in a way that is consistent with the convergence analysis.