Assigning treatment rooms at the Emergency Department

Increasing efficiency at the Emergency Department (ED) reduces overcrowding. At the ED in typical Dutch Hospitals treatment rooms are mostly shared by two residents of different specialties: a Surgeon and an Internist. Each resident uses multiple rooms in parallel; while one patient awaits test results in a treatment room, the resident visits other patients. The assignment of rooms among the residents is often unbalanced, which affects the blocking probability and waiting and sojourn times of patients. Invoking a queueing model in a random environment, we analytically investigate expected sojourn times of (semi-urgent) patients for both types of residents for different room assignment policies and working routines of the residents. We determine the Pareto efficient policies and working routines for all performance measures. We conduct a Discrete Event Simulation to validate our model and present numerical results for a large Dutch teaching hospital and other illustrative cases.