Policies for Physician Allocation to Triage and Treatment in Emergency Departments

In the emergency department (ED), low-acuity patients divert resources from more critical patients. To facilitate flow, EDs are experimenting with new care models, such as the Triage-Treat-and-Release program at the Lutheran Medical Center (LMC) ED in New York, where physicians handle both phases of service for low-acuity patients. Our goal is to determine how physicians in such settings should prioritize triage versus treatment, to balance initial delays with timely discharges. Triage and treatment are modeled as a two-phase stochastic service system, for which an essential feature is patients may leave without receiving treatment. Because patients may choose to leave without receiving treatment, this increases the importance of the second phase. We introduce K-level threshold policies which prioritize treatment unless there are K or more patients in triage. The effect is a class of policies that are flexible enough to capture a decision-maker’s valuation of the importance of each activity; lower K values signifies triage priority. Sufficient conditions are provided to ensure these policies yield a stable system in the sense that the average queue lengths are finite. A heuristic is presented for choosing K in systems with abandonments. Using LMC data, K-level threshold policies, compared to other practical policies, consistently perform well with respect to average rewards and waiting times over a range of parameters. These policies promise physicians an effective and simple way to allocate their time between triage and treatment, without the need for complex model formulation and calibration.