Steady-State Quantile Estimation Using Standardized Time Series

Extending developments of Calvin and Nakayama in 2013 and Alexopoulos et al. in 2019, we formulate point and confidence-interval (CI) estimators for given quantiles of a steady-state simulation output process based on the method of standardized time series (STS). Under mild, empirically verifiable conditions, including a geometric-moment contraction (GMC) condition and a functional central limit theorem for an associated indicator process, we establish basic asymptotic properties of the STS quantile-estimation process. The GMC condition has also been proved for many widely used time-series models and a few queueing processes such as M/M/1 waiting times. We derive STS estimators for the associated variance parameter that are computed from nonoverlapping batches of outputs, and we combine those estimators to build asymptotically valid CIs. Simulated experimentation shows that our STS-based CI estimators have the potential to compare favorably with their conventional counterparts computed from nonoverlapping batches.