Using Queueing Theory to Increase the Effectiveness of Emergency Department Provider Staffing

Abstract

Objectives: Significant variation in emergency department (ED) patient arrival rates necessitates the adjustment of staffing patterns to optimize the timely care of patients. This study evaluated the effectiveness of a queueing model in identifying provider staffing patterns to reduce the fraction of patients who leave without being seen. Methods: The authors collected detailed ED arrival data from an urban hospital and used a Lag SIPP queueing analysis to gain insights on how to change provider staffing to decrease the proportion of patients who leave without being seen. The authors then compared this proportion for the same 39-week period before and after the resulting changes. Results: Despite an increase in arrival volume of 1,078 patients (6.3%), an average increase in provider hours of 12 hours per week (3.1%) resulted in 258 fewer patients who left without being seen. This represents a decrease in the proportion of patients who left without being seen by 22.9%. Restricting attention to a four-day subset of the week during which there was no increase in total provider hours, a reallocation of providers based on the queueing model resulted in 161 fewer patients who left without being seen (21.7%), despite an additional 548 patients (5.5%) arriving in the second half of the study. Conclusions: Timely access to a provider is a critical dimension of ED quality performance. In an environment in which EDs are often understaffed, analyses of arrival patterns and the use of queueing models can be extremely useful in identifying the most effective allocation of staff.