Copyright © 2012 Yingdong Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the performance of a production system with correlated demand through diffusion approximation. The key performance metric under consideration is the extreme points that this system can reach. This problem is mapped to a problem of characterizing the joint probability density of a two-dimensional Brownian motion and its coordinate running maximum. To achieve this goal, we obtain the stationary distribution of a reflected Brownian motion within the positive quarter-plane, which is of independent interest, through investigating a solution of an extended Helmhotz equation.