ORIE Colloquium on 4/9/2013 - Shuangchi He: A One-Dimensional Diffusion Model for Overloaded Queues with Customer Abandonment

ORIE Special Seminar: Shuangchi He (National University of Singapore) - A One-Dimensional Diffusion Model for Overloaded Queues with Customer Abandonment Tuesday, April 9, 2013 at 4:15pm Frank H. T. Rhodes Hall, 253 We use an Ornstein-Uhlenbeck (OU) process to approximate the queue length process for a GI/GI/n+M queue. This simple one-dimensional diffusion model is able to produce accurate performance estimates in two overloaded regimes: In the first regime, the number of servers is large and the mean patience time is comparable or longer than the mean service time; in the second regime, the number of servers can be arbitrary but the mean patience time is much longer (i.e., on a higher order) than the mean service time. We formulate these two regimes into an asymptotic framework where a sequence of queues is considered. The mean patience time goes to infinity in both asymptotic regimes, whereas the number of servers approaches infinity in the first regime but does not change in the second. The OU process is proved to be the diffusion limit for the queue length processes in both asymptotic regimes. A crucial tool for proving the diffusion limit is a functional central limit theorem for the superposition of renewal processes. We prove that the superposition of $n$ independent, identically distributed stationary renewal processes, after being centered and scaled in both space and time, converges to a Brownian motion as $n$ goes large. Bio: Shuangchi is an assistant professor in the Department of Industrial and Systems Engineering at the National University of Singapore. He received his Ph.D. degrees from Georgia Institute of Technology in 2011. His research interests include stochastic modeling and analysis, queueing theory, and statistical signal processing.