Reflected Brownian Motion in an Orthant: Numerical Methods for Steady-State Analysis

Abstract

This paper is concerned with a class of multidimensional diffusion processes, variously known as reflected Brownian motions, regulated Brownian motions, or just RBM's, that arise as approximate models of queueing networks. We develop an algorithm for numerical analysis of a semimartingale RBM with state space $S = \mathbb{R}^d_+$ (the nonnegative orthant of $d$-dimensional Euclidean space). This algorithm lies at the heart of the QNET method for approximate two-moment analysis of open queueing networks.