Central limit theorems for stochastic optimization algorithms using infinitesimal perturbation analysis

Central limit theorems are obtained for the "perturbation analysis Robbins- Monro single run'' (PARMSR) optimization algorithm, with updates either aft er every L customers or after every busy period, in the context of the opti mization of a GI/GI/1 queue. The PARMSR algorithm is a stochastic approxima tion (SA) method for the optimization of infinite-horizon models. It is sho wn that the convergence rate and the asymptotic variance constant of the op timization algorithm, as a function of the total computing budget (i.e., to tal number of customers), are the same for both updating methods, and indep endent of L, provided that the step sizes of SA are chosen in the (asymptot ically) optimal way for each method.