# Slot Optimization Based on Coupled Airspace Capacity of Multi-Airport System
## 4 Algorithm
The common single-airport optimization model fails to consider the constraints affecting airport slot deviation fully and simply takes the minimum slot deviation as the goal, preventing it from making full use of the capacity of each airport and corridor to achieve a fairer and more reasonable slot deviation optimization scheme. (3) The model incorporates China's 24 h coordination parameters and slot firebreaks by dynamically adjusting the capacity-flow ratio during peak-valley cycles, aligning with real-world operational constraints. This study demonstrated that the slot deviation optimization model based on airspace capacity coupling can better balance fairness in multi-airport systems and optimize the utilization of shared airspace capacity resources of each airport, corridor, etc. This model is not only limited to the multi-airport system in the Beijing terminal area but can also be applied to multi-airport systems in other regions of China and the world. There are also many possible directions for future research. Firstly, the research example in this study was a multi-airport system, which can be further expanded to incorporate more corridor capacity. Secondly, airspace capacity constraints under the influence of special weather

Figure 10: (**a**) Scenario 1 corridor flow–capacity ratio diagram; (**b**) Scenario 2 corridor flow–capacity ratio diagram; (**c**) Scenario 3 corridor flow–capacity ratio diagram. (The vertical axis represents the corridor name. The horizontal axis represents the time period of the day, from 0 to 23. The color blocks in the figure represent the flow–capacity ratio, and the values corresponding to the depth are indicated by the color blocks on the right side of the figure. The black block indicates that the flow–capacity ratio exceeds 100%). conditions and other influences can also be explored further. Finally, while this study considered a slot firebreak of 1-2 h, future research can involve more in-depth analysis and validation of the setup time and duration. The proposed model demonstrated high generalizability and extensibility. Regarding capacity parameters, it comprehensively addresses demands across multiple tiers. While encompassing fundamental flight-related parameters, its architecture permits dynamic parameter adjustments (e.g., excluding terminal capacity parameters). This design deliberately accounts for regional bottleneck variations--predominantly flight zones in China versus terminal areas in Europe and North America. Crucially, the model replaces traditional sequential flight coordination (which relies on carrier prioritization systems and suffers from inherent inefficiency) with a global optimization algorithm. This paradigm shift enables the generation of more equitable and efficient bulk slot allocation solutions (providing bundled slot offers), representing a disruptive innovation to existing manual coordination methodologies. This disruptive potential aligns with China's ongoing aviation slot management reform agenda (e.g., online seasonal coordination in favor of computational systems), indicating the model's significant operational viability for use in future slot governance. Engineered explicitly for practical implementation, it contributes to daily slot management, seasonal coordination cycles, and long-term strategic planning (e.g., route network optimization), with primary efficacy in seasonal scheduling. Slot authorities could leverage the model to proactively identify pinned constraints, thereby offering airlines clearer strategic guidance during planning. Furthermore, introduced innovations such as capacity coupling mechanisms and peak/off-peak slot configuration frameworks have substantial research potential. These concepts warrant seamless integration into broader airspace management regimes across tactical, pre-tactical, and flow management phases, extending the model's academic and operational relevance. Conceptualization, S.L., S.W. and L.Y. ; methodology, S.W., S.L. and L.Y. ; software, S.L. and S.W. ; validation, S.L. and S.W. ; formal analysis, S.L.