Diffusion approximations for many-server queues have been studied extensively since the pioneering work of Halfin and Whitt (1981). We focus on many-server queues that have phase-type service time distributions and exponential customer patience distributions. We establish rate of convergence of the steady-steady distribution of a many-server queue in the Halfin-Whitt regime. Our proof technique connects naturally with Stein's method for establishing normal approximations. This connection allows us to extend the recent work of Gurvich (2014).
This is the joint work with Jim Dai at Cornell University.