Optimal control of an emergency room triage and treatment process

Gabriel Zayas-Cabán
Center of Applied Mathematics

Cornell University

Ithaca, NY 14853

Jingui Xie

School of Management

University of Science and Technology of China

Linda V. Green

Graduate School of Business

Columbia University

Mark E. Lewis

School of Operations Research & Information Engineering
Cornell University
Ithaca, NY 14853

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.