Optimal Control of an Emergency Room Triage and Treatment Process

Abstract

Patient care in many healthcare systems consists of two phases of service: assessment (or triage) and treatment. It is sometimes the case that these phases are carried out by the same medical providers. We consider the question of how to prioritize the work by the medical providers to balance initial delays for care with the need to discharge patients in a timely fashion. To address this question, we present a multi-server two-stage tandem queueing model for a hospital emergency department (ED) triage and treatment process. We assume that all patients first receive service (i.e. triage) from the first station. After completing this service some patients leave the system for some other part of the ED. The remaining patients are served or await service from the second station where they may abandon before receiving treatment. We use a Markov decision process formulation and sample path arguments to determine the optimal dynamic policy for the medical service provider.

In particular, we show that there exists optimal control policies that do not idle servers when there is work available and do not split servers except to avoid idling. We then focus on the states that have more patients than there are medical service providers. We consider a single server model as an approximation for these states and provide conditions under which it optimal to prioritize phase-one service (triage) or phase-two service (treatment). In addition, we introduce a new class of threshold policies as alternatives to priority rules. Using data from an actual hospital, we compare the performance of all of the aforementioned policies and several other potential service policies in a simulation study. Results show that for a wide range of parameter values, the threshold service disciplines perform well.

Keywords: ER treatment process; optimal control, single-server tandem queue