Efficient Input Uncertainty Quantification for Regenerative Simulation

Abstract

The initial bias in steady-state simulation can be characterized as the bias of a ratio estimator if the simulation model has a regenerative structure. This work tackles input uncertainty quantification for a regenerative simulation model when its input distributions are estimated from finite data. Our aim is to construct a bootstrap-based confidence interval (CI) for the true simulation output mean performance that provides a correct coverage with significantly less computational cost than the traditional methods. Exploiting the regenerative structure, we propose a $k$-nearest neighbor ($k$NN) ratio estimator for the steady-state performance measure at each set of bootstrapped input models and construct a bootstrap CI from the computed estimators. Asymptotically optimal choices for $k$ and bootstrap sample size are discussed. We further improve the CI by combining the $k$NN and likelihood ratio methods. We empirically compare the efficiency of the proposed estimators with the standard estimator using queueing examples.