## 5 Conclusions  
This study introduces a sophisticated approach for the modeling and analysis of railway station yard diagrams based on multi-layer complex network theory, addressing the critical challenge of identifying key constraints on station throughput capacity within the limitations of existing infrastructure. By transforming railway station yard data into a complex network representation and utilizing various matrix forms--such as adjacency matrix, structural matrix, connection count matrix, and transition probability matrix--the method effectively encapsulates the complex interrelations among track segments. The node importance evaluation is conducted through the development and application of advanced metrics, including node connectivity strength, destination and source node count, node efficiency, and an extended PageRank algorithm based on edge weights. Additionally, a dual-layer evaluation framework is proposed, encompassing single-metric stratified network analysis and multi-layer network comprehensive assessment. The proposed methodology is validated through a case study on a typical conventional railway station. A more rigorous analysis of each evaluation indicator was conducted, along with an in-depth discussion on the application of the integrated assessment method based on Principal Component Analysis and rank-sum ratio (PCA-RSR). The findings indicate that the proposed approach effectively identifies critical nodes constraining throughput capacity, offering valuable insights for optimizing operational efficiency and enhancing overall system performance. This research provides a robust analytical framework for railway network optimization, with significant contributions to both theoretical advancements and practical applications in railway operations management. This study presents a structured evaluation of railway station throughput capacity based on a fully operational network model. The proposed framework effectively identifies key track sections that constrain throughput, providing valuable insights for optimizing station operations. However, it does not incorporate disruptions arising from infrastructure failures, track maintenance, or signaling malfunctions. To enhance the robustness of the methodology, future research should explore dynamic failure modeling, stochastic disruption analysis, and risk-aware node importance evaluation, ensuring that railway station optimization considers both efficiency and functional safety. Addressing the critical challenge of identifying key constraints on station throughput capacity within existing infrastructure limitations is not only fundamental for improving station operations and overall network performance but also has significant implications for cost management [32] and RAMS (reliability, availability, maintainability, and safety) [67]. While throughput optimization remains a primary objective, the proposed methodology extends beyond capacity improvements by offering valuable insights into infrastructure sustainability and long-term operational efficiency. By accurately identifying critical track sections, maintenance efforts can be more strategically allocated, thereby reducing failure risks and enhancing system reliability [67]. Moreover, optimizing the utilization of key nodes improves operational availability and strengthens station resilience against disruptions. These enhancements contribute to a more robust and cost-effective railway network, mitigating the financial and operational risks associated with unplanned failures. Building upon previous studies that have established methodologies for estimating infrastructure costs in high-speed and high-capacity railways, this study develops a model to identify track sections with high occupancy rates [32]. Optimizing operational strategies for these critical constraints can increase daily tonnage, which, in turn, affects both track maintenance requirements and overall infrastructure costs.