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Queueing Models for Patient-Flow Dynamics in Inpatient Wards

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Document pages: 53 pages

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.

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