# Slot Optimization Based on Coupled Airspace Capacity of Multi-Airport System
## 1 Introduction
We summarize the relevant literature in Table 1.  
Based on the above research, one of the core problems of airport slot optimization is capacity utilization; however, most of the existing research is based on the announced capacity for analysis, combined with the actual situation of the civil aviation transportation industry at this stage. The interactions between multi-airport systems need to be expanded from the independent capacity of a single airport to the coupled capacity between multiple airports. Therefore, the spatial characteristics of airspace capacity and the temporal characteristics of flights should be fully considered during the research process, and the airspace unit's capacity should be restrained and refined to propose realistic and practical solutions for airport slot optimization. Research on the collaborative optimization of airport slot allocation in multi-airport systems has indicated that the objective of optimization generally focuses on a single objective, such as delay or slot deviation minimization, while some studies have explored the fairness of airports and airlines, integrating efficiency and fairness into the objective function. The focus is mainly on nine constraints. The all-day time coordination parameter defines hourly or 15 min airport capacity limits. Single-airport capacity constraints set maximum flight handling limits per airport. Sector capacity controls airspace zone volumes, while corridor opening capacity restricts aircraft flow through designated airways. Ground resource constraints cap apron usage capacity at airports. Additionally, sector and corridor port capacity determine maximum throughput at critical airspace nodes. Crucially, multi-airport coupling constraints govern the shared capacity between system airports. Finally, capacity-flow uncertainty ratios address planning-stage estimation errors in airport slots and taxiing times. These errors induce spatio-temporal resource mismatches, potentially causing flight delays or underutilized airspace capacity. Although most of the existing models include some of the above constraints, there is room for improvement in terms of their completeness and practical compliance. Firstly, the assumption of singularity of capacity is inconsistent with the characteristics of multi-airport system airspace resources that can be shared, and many studies have failed to consider the  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Reference** & **Model Objectives** & & & & & & **Constraints** & & & & \\  & & **24 h Coor-** & **Airport** & **Sector** & **Ground** & **Multi-Airport** & **Corridor** & **Ratio of** & **Flight** & **Acceptable** \\  & & **Parameters** & **Capacity** & **Capacity** & **R-** & **Coupling** & **Port Ca-** & **the** & **Transit** & **Slot Deviation** \\  & & & & & & **Capacity** & **Pacity** & **Flow** & & & \\ \hline
[15] & Minimize total deviation & & \(\surd\) & \(\surd\) & & & & & & & \\  & Minimize the & & & & & & & & & \\  
variability of airport capacity under the airspace-capacity coupling relationship. Secondly, most of the current fairness considerations stem from the perspective of the interests of the air carrier, and there is a lack of operational-level considerations. The fairness measure based on operational indicators has not yet been integrated. Considering only the number of slots of the carrier at the coordinated airport as a benchmark for measuring fairness is not comprehensive enough and may lead to the unnecessary deviation of flights during off-peak hours. Doing so not only increases the difficulty of slot coordination but is also unreasonable. Thirdly, the uncertainty of capacity-flow matching in the process of flight operation at a multi-airport system may lead to mismatches of other spatial-temporal resources, which can cause, for example, delays, insufficient airspace capacity, and a lack of airspace capacity.