# Slot Optimization Based on Coupled Airspace Capacity of Multi-Airport System
## 4 Algorithm
Comparing the airport fairness and airline congestion contribution fairness based on different optimization methods (Table 4) shows that the optimization results of the multi-airport system are all better than the single-airport optimization results, which indicates that more constraints and stronger constraints of the multi-airport model make the optimization of the multi-airport system more reasonable. ### Simulation Verification

#### 5.5.1 Simulation Environment Settings

Due to operational security limitations, computer simulations were used for verification. Using the AirTOp software, a computer simulation model containing the capital, Daxing, and Tianjin airports was set up with structural static parameters such as waypoints, routes, flight procedures, sectors, and other parameters of the multi-airport system airspace, as well as control operation parameters and operation rule parameters in accordance with the operation rules. The simulation model passed the calibration of the air traffic management department, and the simulation airspace environment included the capital city, Daxing, and Tianjin airports, which is a northbound operation and does not contain other airspace user activities. #### 5.5.2 Implementation of the Simulation

**Scenario 1:**: _Base timetable as input for simulation._
**Scenario 2:**: _Three timetables optimized for the single-airport system as input for Scenario 2._
**Scenario 3:**: _Optimized multi-airport timetable as input for Scenario 3 flight planning. A total of 31 computer simulations were performed for each scenario. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Optimization** & \multirow{2}{*}{**Slot Deviation**} & \multirow{2}{*}{**Airport Fairness**} & **Airline Congestion** \\
**Method** & & & **Contribution** \\  & & & **Fairness** \\ \hline Multi-airport & 35,535 & 0.009 & 13.615 \\ Single airport & 33,440 & 0.018 & 18.044 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of results. Figure 8: Comparison of frequencies and cumulative probabilities of multi-airport and single-airport optimization (refer to Figure 6 for more details). #### 5.5.3 Simulation Results

(1) Simulation delay analysis

The simulated delay results for the three scenarios are presented in Table 5. The main outputs of the simulation are the arrival delay, departure delay, and average delay for each airport. The flight arrival delays refer to the delays caused by aircraft in the terminal area due to sequencing, scheduling, etc. ; the flight departure delays refer to the delays caused by aircraft due to runway waiting, slot waiting, etc. ; and the average delays refer to the average delays incurred by aircraft at the airport. Table 5 shows the average arrival delay, average departure delay, and average delay of the three scenarios. Based on the results of the multi-airport optimization, all three airports have low delays compared with the single-airport optimization; therefore, the multi-airport optimization simulation is the best. (2) Sector capacity-flow relationship analysis

Sector flows from the 16 th simulation are taken for airport flow-capacity ratio analysis, as shown in Figure 9. In Scenario 1 with no optimization, seven sectors are involved, and overcapacity occurs in 19 time slots; in Scenario 2 with single-airport schedule optimization, seven sectors are involved, and overcapacity occurs in 24 time slots; and in Scenario 3 with multi-airport schedule optimization, no overcapacity occurs in the sectors. The overcapacity results in delays due to the deployment that occurs in the simulation.