Through queueing systems modeling customer call centers and hospital patient flows, I will give an introduction on how to use Stein’s method both as an engineering tool for generating good steady-state approximations and as a mathematical too for establishing error bounds of these approximations. These approximations are often universally accurate in multiple parameter regions, from underloaded, to critically loaded, to overloaded (when customers abandon). I will focus on diffusion models for performance analysis. Time permitting, I will also briefly discuss related works by Gurvich and his collaborators on ergodic optimal controls and by Ying on mean-field approximations.

The talk is based on joint works with Anton Braverman, Jiekun Feng, and Pengyi Shi.