Stein's Method for Steady-state Diffusion Approximations

Thursday, June 25, 2015 - 9:15am - 10:15am
Keller 3-180
Jim Dai (Cornell University)
I will introduce a modular framework for proving the rate of convergence for approximating the stationary distribution of a stochastic processing network by the stationary distribution of its
corresponding diffusion model. The framework is based on Stein's method and extends a recent work of Gurvich (2014). I will illustrate the framework in detail using two classes of queues: M/M/n+M queues in which customers have iid patience times that are exponentially distributed
and M/Ph/n+M queues in which service times have a phase-type distribution. I will also discuss recent progress on generalized Jackson networks in which the corresponding diffusion models are
multidimensional semimartingale reflecting Brownian motions (SRBMs) that were first introduced in Harrison and Reiman (1981). This talk is based joint work with Anton Braverman at Cornell.