Queueing Models for Patient-Flow Dynamics in Inpatient Wards

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 nonstationary 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 the 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.