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Variance and derivative estimation for virtual performance in simulation analytics

Virtual performance is a class of time-dependent performance measures conditional on a particular event occurring at timet0 for a (possibly) nonstationary stochastic process; virtual waiting time of a customer arriving to a queue at time t0 is one example. Virtual statistics are estimators of the virtual performance. In this paper, we go beyond the mean to propose estimators for the variance, and for the derivative of the mean with respect to time, of virtual performance, examining both their small-sample and asymptotic properties. We also provide a modified K-fold cross validation method for tuning the parameter k for the difference-based variance estimator, and evaluate the performance of both variance and derivative estimators via controlled studies. The variance and derivative provide useful information that is not apparent in the mean of virtual performance.