Emergency department (ED) overcrowding has been a prevalent issue for several decades in hospitals around the world. Particularly, ED crowding generally reduces the quality of care, increases the waiting time of patients or induces dissatisfaction for the physicians. The prioritization policy between patients influences this process. Therefore, developing patient allocation models can improve the operation of EDs.

A common practice in EDs around the world is to use a triage system to allocate resources and provide guidelines for classifying patients into priority groups (triage levels) based on their acuity, urgency, and resource needs. Hence, current prioritization models may depend solely on the severity of a patient but not on the complexity of the service. However, it has been shown that ED operations can be improved by incorporating both the complexity and urgency information of the patients into the scheduling decisions.

In this work, we propose a patient allocation model incorporating consultation time predictions. The ED is modeled as a queuing system. We then simulate the operations of the ED using a large set of data from a University Hospital in Montreal. This data is also used to train a model for predicting consultation time probability densities. We propose several allocation policies that use the consultation time predictions and aim to reduce a given cost. These allocation policies are compared to benchmark policies that are found in the literature on similar problems.