Abstract:

Objective To construct a quantitative relationship model between the number of emergency triage windows and patient arrival rates，and to propose dynamic optimization strategies for multiple scenarios，thereby providing a data-driven decision-making tool for emergency workforce allocation. Methods A retrospective analysis was conducted on the full-year 2024 emergency department data from a tertiary-grade A hospital in Shanghai. Based on the multi-queue multi-server M/M/S queuing model，a static calculation formula for the optimal number of triage windows was derived. Subsequently，Anylogic simulation software was employed to construct a dynamic simulation model covering three typical scenarios—routine triage，ambulance surge，and febrile patient diversion—to validate and refine the static formula. Finally，a three-level graded load response strategy was proposed based on the simulation results. Results Patient arrivals exhibited diurnal and seasonal bimodal peaks，with an average triage service time of （127.56±26.48） seconds. For the routine triage scenario，a linear configuration function was fitted：y= 0.035x+0.5，where y represents the number of triage nurses and x denotes the number of patient arrivals per hour. Simulation validation showed an overall root mean square percentage error（RMSPE） of 4.5%，outperforming the static model alone（RMSPE=12.3%）. For the ambulance surge scenario，a bivariate dynamic formula was proposed：N_windows=λ/30+0.3·P_ambulance·λ（where P_ambulance represents the proportion of ambulance arrivals），which reduced offload delay by 46.9% compared with the static formula. For the febrile patient diversion scenario，owing to increased screening complexity，the window requirement followed a quadratic function：N_windows=0.000 08λ²+ 0.016λ+1.2. Conclusion The integrated “static plus dynamic” model developed in this study provides a quantifiable，progressive decision-making tool for emergency triage workforce allocation，facilitating the transition of emergency management from experience-driven to data-driven approaches. As a single-center retrospective study，the generalization of the model to non-tertiary hospitals and other regions requires further validation. Future multicenter studies incorporating cost-effectiveness analysis are warranted to optimize model parameters and promote broader applicability.

Key words: Emergency Department, Pre-Examination and Triage, Queuing Theory, Resource Allocation, Anylogic Simulation, Nursing Management Research