On comparison of steady-state infinitesimal perturbation analysis and likelihood ratio derivative estimates

In this paper, we compare the infinitesimal perturbation analysis (IPA) and likelihood ratio (LR) derivative estimators for the steady-state system time of the M/M/1 queue. We derive the explicit formulas for the variances of both estimators. We then show IPA has smaller variance, which is often considered as a rule-of-thumb in the simulation literature. This is the first theoretical result that proves IPA has smaller variance than LR for steady-state performance measures.