Steady-state quantile parameter estimation: An empirical comparison of stochastic kriging and quantile regression

The time required to execute simulation models of modern production systems remains high even with todays computing power, particularly when what-if analyses need to be performed to investigate the impact of controllable system input variables on an output performance measure. Compared to mean and variance which are frequently used in practice, quantiles provide a more complete picture of the performance of the underlying system. Nevertheless, quantiles are more difficult to estimate efficiently through stochastic simulation. Stochastic kriging (SK) and quantile regression (QR) are two promising metamodeling tools for addressing this challenge. Both approximate the functional relationship between the quantile parameter of a random output (e.g., cycle time) and multiple input variables (e.g., start rate, unloading times). In this paper, we compare performances of SK and QR on steady-state quantile parameter estimation. Results are presented from simulations of an M/M/1 queue and a more realistic model of a semiconductor manufacturing system.