Five easy equations for patient flow through an emergency department

Area of Science:

• Healthcare Management
• Operations Research
• Biostatistics

Background:

• Queue models offer valuable frameworks for management decisions in healthcare settings.
• Danish hospitals can benefit from understanding and applying queueing theory.
• Emergency departments (EDs) are undergoing reorganization, making timely empirical investigation of queue models relevant.

Purpose of the Study:

• To empirically investigate the applicability and relevance of the standard "M/M/1" queue model in Danish emergency departments.
• To document the utility of queue modeling for ED management during reorganization.

Main Methods:

• Compared actual versus theoretical hourly patient flow distributions from 27,000 patient cases at Frederiksberg Hospital's ED.
• Developed and tested a five-equation simulation model based on arrival and capacity equations.

Main Results:

• Patient arrivals followed a Poisson distribution with an hour-specific parameter.
• Treatment times exceeding 15 minutes were described by an exponential distribution.
• ED capacity was found to be relatively constant despite staffing variations, fitting the M/M/1 model.
• A compact framework was formulated for assessing ED behavior under different operational assumptions.

Conclusions:

• The M/M/1 queue model demonstrated a near-perfect fit for the studied emergency department.
• Modeling and simulations proved to be valuable tools contributing to the ED management process.