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This note details the development of a discrete-time diffusion process toapproximate the midnight customer count process in a$M_\textrm{per}/\textrm{Geo}_\textrm{2timeScale}/N$ system. We prove a limittheorem that supports this diffusion approximation, and discuss two methods tocompute the stationary distribution of this discrete-time diffusion process.

Technical Note for Discrete-Time Diffusion Approximations Motivated from Hospital Inpatient Flow Management