## 5 Conclusions
This ensures that they can make quick and accurate decisions in emergency situations;
* Emphasize Language Training: especially in the international aviation sector, where English is the universal language of aviation, it is crucial to focus on the English communication skills of controllers and pilots to ensure effective communication on international routes. Additionally, considering the importance of native languages, it is advisable to encourage and support the use of native languages for communication wherever possible. This can further improve the accuracy and efficiency of information transmission;
* Upgrade Technical Support: continually update aviation management systems and tools, such as automated conflict detection and resolution systems. These enhancements can significantly improve the efficiency of controllers and pilots in managing safety. These systems are capable of real-time monitoring of flight paths, predicting potential conflicts and risks, thereby allowing controllers and pilots to take preventive actions to avoid accidents. In summary, assessing collision risks for intersecting flight routes in different scenarios and determining a safe separation at a given TLS can effectively enhance the safety of aircraft operations. This has several benefits: (1) Optimizing airspace traffic allocation: Utilizing the results of safe separation calculations helps to manage air traffic flow more efficiently. This reduces congestion on air routes, enhances overall efficiency in airspace operations, and optimizes the allocation of traffic within the airspace; (2) Supporting the implementation of new air traffic management technologies: In the realm of new air traffic management technologies, such as automation, advanced navigation systems, and communication technologies, determining safe separation is crucial. It provides a theoretical foundation for the application of these new technologies, ensuring their safety and feasibility; (3) Enhancing airspace utilization efficiency: Through precise assessment of collision risks, there is an opportunity to more effectively utilize airspace, increase traffic flow, expand network capacity, and align it with the capabilities of air transportation. These measures contribute to ensuring that aircraft operations in the airspace are not only safer and more efficient but also provide essential support for the future development of air traffic management. Finally, when analyzing the impact of controllers and pilots' operational time on collision risk, the direct use of enumeration methods to simulate different human-operated adjustment times failed to match with operator types corresponding to different behavioral characteristics. Future research should delve deeper and offer more targeted suggestions to further enhance the safety levels of aircraft operations in air spaces. **Funding:** This research was funded by National Natural Science Foundation of China (Grant 52272356) and Fundamental Research Funds for the Central Universities (Grant 3122022101). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study. **Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. **Conflicts of Interest:** The authors declare no conflicts of interest.