A Markov decision optimization of medical service resources for two-class patient queues in emergency departments via particle swarm optimization algorithm.

In the modern healthcare system, the rational allocation of emergency department (ED) resources is crucial for enhancing emergency response efficiency, ensuring patient safety, and improving the quality of medical services. This paper focuses on the issue of ED resource allocation and designs a priority sorting system for ED patients. The system classifies patients into two queues: urgent and routine. Considering different service rates, a multi-server preemptive priority queueing model [Formula: see text] and a multi-server non-preemptive priority queueing model [Formula: see text] are constructed. Additionally, the number of beds, K, is introduced as the capacity of the urgent queue. By comprehensively considering the costs associated with patient waiting time, the cost of rejecting the most critical patients, and the total costs of beds and servers, a mixed-integer programming model was constructed with the objective of minimizing the total cost. The particle swarm optimization algorithm was applied to determine the optimal number of servers, service rate, and number of beds. Compared with the model proposed by Alipour-Vaezi et al., our model significantly improves patient waiting times and queue lengths using the same data set: the waiting time [Formula: see text] decreased by 74.44%, [Formula: see text] by 5.79%, and [Formula: see text] by 1.13%; the queue length [Formula: see text] decreased by 78% and [Formula: see text] by 3.33%. Our model effectively reduces patient waiting times and queue lengths while controlling costs, identifies the optimal number of beds, and achieves optimized resource allocation. Finally, we conducted a sensitivity analysis and provided some valuable management insights.