International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 109417, 12 pages
Research Article

Performance Analysis of Production Systems with Correlated Demand via Diffusion Approximations

Business Analytics and Mathematical Sciences, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA

Received 9 August 2012; Revised 19 December 2012; Accepted 19 December 2012

Academic Editor: Enzo Orsingher

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.


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.