Emergency department (ED) overcrowding and patient boarding represent critical systemic challenges that compromise care quality. We propose a threshold-based admission policy that redirects non-urgent patients to alternative care pathways, such as telemedicine, during peak congestion. The ED is modeled as a two-class $M/M/c$ preemptive-priority queuing system, where high-acuity patients are prioritized and low-acuity patients are subject to state-dependent redirection. Analyzed via a level-dependent Quasi-Birth-Death (QBD) process, the model determines the optimal threshold by maximizing a long-run time-averaged objective function comprising redirection-affected revenue and costs associated with patient balking and system occupancy. Numerical analysis using national healthcare data reveals that optimal policies are highly context-dependent. While rural EDs generally optimize at lower redirection thresholds, urban EDs exhibit performance peaks at moderate thresholds. Results indicate that our optimal policy yields significant performance gains of up to $4.84\%$ in rural settings and $5.90\%$ in urban environments. This research provides a mathematically rigorous framework for balancing clinical priority with operational efficiency across diverse ED settings.

翻译：急诊科（ED）过度拥挤与患者滞留是影响医疗质量的关键系统性挑战。本文提出一种基于阈值的分诊策略，在高峰拥堵期将非急症患者分流至替代性护理路径（如远程医疗）。我们将急诊科建模为两类$M/M/c$抢占式优先级排队系统，其中高危急患者享有优先权，低危急患者则根据系统状态进行分流。通过层级依赖的拟生灭过程（QBD）进行分析，该模型以最大化长期时间平均目标函数为目标确定最优阈值，该函数综合考量了分流相关收益、患者放弃就诊成本及系统占用成本。基于全国医疗数据的数值分析表明，最优策略具有高度情境依赖性：农村急诊科通常在较低分流阈值处实现优化，而城市急诊科则在中等阈值处呈现性能峰值。结果显示，最优策略在农村环境中可实现高达$4.84\%$的性能提升，在城市环境中可达$5.90\%$。本研究为在不同急诊科场景中平衡临床优先级与运营效率提供了数学严谨的决策框架。