Performance evaluation for the score function method in sensitivity analysis and stochastic optimization

Abstract

Estimating systems performance 𝓁(ρ) = 𝔼 _ρ L and the associated sensitivity (the gradient ∇𝓁(ρ)) for several scenarios via simulation generally requires a separate simulation for each scenario. The score function (SF) method handles this problem by using a single simulation run, but little is known about how the estimators perform. Here we discuss the efficiency of the SF estimators in the setting of simple queueing models. In particular we consider heavy traffic (diffusion) approximations for the sensitivity and the variances of the associated simulation estimators, and discuss how to choose a ‘good’ reference system (if any) in order to obtain reasonably good SF estimators.