An Efficient Budget Allocation Approach for Quantifying the Impact of Input Uncertainty in Stochastic Simulation

Simulations are often driven by input models estimated from finite real-world data. When we use simulations to assess the performance of a stochastic system, there exist two sources of uncertainty in the performance estimates: input and simulation estimation uncertainty. In this article, we develop a budget allocation approach that can efficiently employ the potentially tight simulation resource to construct a percentile confidence interval quantifying the impact of the input uncertainty on the system performance estimates, while controlling the simulation estimation error. Specifically, nonparametric bootstrap is used to generate samples of input models quantifying both the input distribution family and parameter value uncertainty. Then, the direct simulation is used to propagate the input uncertainty to the output response. Since each simulation run could be computationally expensive, given a tight simulation budget, we propose an efficient budget allocation approach that can balance the finite sampling error introduced by using finite bootstrapped samples to quantify the input uncertainty and the system response estimation error introduced by using finite replications to estimate the system response at each bootstrapped sample. Our approach is theoretically supported, and empirical studies also demonstrate that it has better and more robust performance than direct bootstrapping.