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

TL;DR

This paper develops a discrete-time diffusion model to approximate hospital inpatient flow, providing theoretical support and methods for stationary distribution computation, aiding better capacity planning.

Contribution

It introduces a novel discrete-time diffusion approximation for hospital inpatient flow and proves a limit theorem supporting its validity.

Findings

Proves a limit theorem for the diffusion approximation.

Provides two methods to compute stationary distributions.

Enhances modeling accuracy for 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 $M_\textrm{per}/\textrm{Geo}_\textrm{2timeScale}/N$ 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.