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

Abstract

This note details the development of a discrete-time diffusion process to approximate the midnight customer count process in a $M_{\text{per}}/{\text{Geo}}_{\text{2timeScale}}/N$ 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.

arXiv comment15 pages