Efficient Steady-State Simulation of High-Dimensional Stochastic Networks

Abstract

We propose and study an asymptotically optimal Monte Carlo estimator for steady-state expectations of a d-dimensional reflected Brownian motion (RBM). Our estimator is asymptotically optimal in the sense that it requires [Formula: see text] (up to logarithmic factors in d) independent and identically distributed scalar Gaussian random variables in order to output an estimate with a controlled error. Our construction is based on the analysis of a suitable multilevel Monte Carlo strategy which, we believe, can be applied widely. This is the first algorithm with linear complexity (under suitable regularity conditions) for a steady-state estimation of RBM as the dimension increases.