Traffic Intensity of Patients and Physicians in the Emergency Department: A Queueing Approach for Physician Utilization

Background: The unpredictable nature of patient visits poses considerable challenges to the staffing of emergency department (ED) medical personnel. There is a lack of common physician usage parameters at present. Objective: The aim of this study was to quantify the ED traffic intensity of patients and physicians using a queueing model approach. Methods: A retrospective administrative electronic data analysis was conducted in a tertiary medical center. All patients who registered at the ED in 2013 were included. Precisely recorded patient waiting time, service time, and disposition time were obtained. An M/M/s (Markovian patient arrival, Markovian patient service, s servers) queueing model was used, while taking account of the actual physician number and number of patients managed simultaneously. Physician utilization and performance indicators were measured. Results: A total of 148,581 patients were analyzed after exclusion. The overall mean waiting time, service time, and disposition time were 0.23 (standard deviation [SD] = 0.24), 2.31 (SD = 3.89), and 2.54 (SD = 3.90) hours, respectively. Hourly physician utilization (ρ), stratified by different patient entities, was ρ = 0.75 ± 0.17 for adult non-trauma, ρ = 0.75 ± 0.28 for pediatric, and ρ = 0.53 ± 0.18 for trauma (p = 0.0004). There was a surge of utility for pediatric non-trauma patients in the late evening (ρ = 1.4 at 11 PM). The distribution of number of patients in the system was derived and compared by different patient entities and time points. Conclusions: A queueing model was built to model traffic intensity of physicians and patients, the physician utility trend disclosed the fluctuation of manpower utility. The estimated parameters serve as important factors for developing tailored staffing policies for minimizing ED waiting and improving ED crowding.