Variance reduction for sensitivity estimates obtained from regenerative simulation

Abstract

We apply the method of concomitant control variables to reduce the variance of derivative estimates obtained from regenerative simulations using the likelihood ratio method. We restrict our attention to systems that contain a Poisson process. The control variables that we use arise naturally from likelihood ratios. After deriving an expression for the optimal coefficients of the control variables, we numerically investigate their performance. Using six controls with an M/G/1 queue we achieve a reduction in the standard deviation of the derivative estimate of up to 60%.