Optimizing the Capacity Allocation of the Chinese Hierarchical Healthcare System under Heavy Traffic Conditions

In this study, we explore optimal service allocation within the Chinese hierarchical healthcare system with green channels, providing valuable insights for practitioners to understand how optimal service allocation is affected by various realistic factors. These green channels are designed to streamline referrals from community healthcare centers to comprehensive hospitals. We aim to determine the optimal capacity allocation for these green channels within comprehensive hospitals. Our research employs techniques from queuing theory and stochastic processes, e.g., diffusion analysis, to develop a mathematical model that approximates the optimal allocation of resources. We uncover both closed-form and numerical solutions for this optimal capacity allocation. By analyzing the impact of various cost factors, we find that an increase in costs within the green channel results in a lower optimal service rate. Additionally, patient preferences for specific treatments influence allocation, reducing the optimal share of services provided by general hospitals. The optimal solution is also affected by the proportions of different patient types. Through extensive simulations, we validate the accuracy of our model approximations under heavy traffic conditions, further examining sources of error to ensure robustness. Our findings provide valuable insights into optimizing resource allocation in hierarchical healthcare systems, ensuring efficient and cost-effective patient care.