We investigate the crucial and complex task of selecting patients by physicians in emergency departments when multiple patient types are present. Conventional approaches in guiding physician decision-making are based on patient triage levels or waiting times. However, an important factor that is often overlooked is the time remaining in a physician's shift. We utilize a transient optimal control on the corresponding queueing system to derive an optimal time-dependent patient selection strategy.

Given heterogeneous treatment time distributions, no-shows, and patients that can arrive early or late, we show how a discrete time Markov chain model can be used to equitably space patients so that no patient has an expected wait longer than some maximum value. The calculation of an equitable schedule can be done extremely fast, in polynomial time, involving only simple linear algebra (matrix multiplication). The equitable schedule adds at most 2% to the clinic’s operation time.

Emergency Department (ED) boarding refers to the delay in transfer experienced by admitted patients from the ED to inpatient units. Using an instrumental variable design, we found that, on average, longer boarding time leads to a longer hospital stay and a higher chance of care escalation. Our findings also reveal that the impact of boarding differs across patients, suggesting that considering such heterogeneity when assigning inpatient beds could improve downstream efficiency and quality of care