%0 Journal Article %T Technical Note for Discrete-Time Diffusion Approximations Motivated from Hospital Inpatient Flow Management %A J. G. Dai %A Pengyi Shi %J Mathematics %D 2015 %I arXiv %X This note details the development of a discrete-time diffusion process to approximate the midnight customer count process in a $M_\textrm{per}/\textrm{Geo}_\textrm{2timeScale}/N$ system. We prove a limit theorem that supports this diffusion approximation, and discuss two methods to compute the stationary distribution of this discrete-time diffusion process. %U http://arxiv.org/abs/1508.05148v1