Diffusion Approximations and Optimal Control of Queueing Systems in Heavy-Traffic

Ananda Weerasinghe
Iowa State University
Professor of Mathematics

“The method of diffusion approximations provides a powerful tool to analyze complex queueing systems under “heavy traffic conditions.’’ We first introduce such a class of queueing systems and the approximating diffusion process. Then we present a cost minimization problem for an infinite-server queueing system with controlled service rates. The cost structure depends on the running maximum of the number of customers in the system as well as the controlled service rate. We employ the diffusion approximation theory to formulate an approximating diffusion control problem (DCP). Next we carefully analyze the corresponding Hamilton-Jacobi-Bellman equation and construct a sufficiently smooth solution for it. Consequently, we use this solution to obtain a bounded feedback type optimal control process for the DCP. Finally, we use it to obtain a nearly optimal solution for the queueing control problem.”

Light refreshments will be served @ 1:30PM in EMS E424A.