Efficient Input Uncertainty Quantification for Regenerative Simulation

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 (kNN) 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 kNN and likelihood ratio methods. We empirically compare the efficiency of the proposed estimators with the standard estimator using queueing examples.