Queueing Models for Patient-Flow Dynamics in Inpatient Wards

44 Pages Posted: 28 Sep 2018

See all articles by Jing Dong

Jing Dong

Columbia University

Ohad Perry

Northwestern University - Department of Industrial Engineering and Management Sciences

Date Written: September 9, 2018

Abstract

Hospital-related queues have unique features that are not captured by standard queueing assumptions, necessitating the development of specialized models. In this paper we propose a queueing model that takes into account the most salient features of queues associated with patient-flow dynamics in inpatient wards, including the need for a physician's approval to discharge patients, and subsequent discharge delays. In this setting, fundamental quantities, such as the (effective) mean hospitalization time and the traffic intensity, become functions of the queueing model's primitives. We therefore begin by characterizing these quantities, and quantifying the impacts that the discharge policy has on the average bed utilization and maximal throughput. We then introduce a deterministic fluid model to approximate the non-stationary patient-flow dynamics. The fluid model is shown to possess a unique periodic equilibrium, which is guaranteed to be approached as time increases, so that long-run performance analysis can be carried out by simply considering that equilibrium cycle. Consequently, evaluating the effects of policy changes on system's performance, and optimizing long-run operating costs, are facilitated considerably. The effectiveness of the fluid model is demonstrated via comparisons to data from a large hospital and simulation experiments.

Keywords: Patients-Flow; Discharge Delays; Multi-Server Queue with Blocking; Deterministic Fluid Approximations; Long-Run Periodicity

Suggested Citation

Dong, Jing and Perry, Ohad, Queueing Models for Patient-Flow Dynamics in Inpatient Wards (September 9, 2018). Available at SSRN: https://ssrn.com/abstract=3246641 or http://dx.doi.org/10.2139/ssrn.3246641

Jing Dong (Contact Author)

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Ohad Perry

Northwestern University - Department of Industrial Engineering and Management Sciences ( email )

2145 Sheridan Road
Room C210
Evanston, IL 60208
United States

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