# A Study on the Normalized Delineation of Airspace Sectors Based on Flight Conflict Dynamics
## 5 Validation and Analysis of Sectorization Algorithms
### Analysis of Sectorization Results  
In order to prove the reasonableness of the delineation of sectors by distinguishing busy/idle time segments, the radar data of any busy and idle time segments are selected to calculate the integrated network indexes of sectors before and after the delineation, and the standard deviation of the integrated network indexes of sectors are compared, and the results obtained are shown in Figure 10.  
As can be seen from Figure 10, whether it is idle time segment or busy time segment, the integrated network index of each sector after the delineation is more balanced relative to the pre-delineation period, and the integrated network index of busy time segment sectors numbered 1-4 is changed from the original {1.421, 1.225, 1.254, 1.562} to the current {1.365, 1.294, 1.140, 1.387}; the integrated network index of each sector standard deviation is reduced by 40.4% compared to the original sector. The integrated network index of idle time segment and busy time segment numbering 1-4 has changed from the original {0.542, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Serial Number** & **Coordinate** & **Serial Number** & **Coordinate** \\ \hline
1 & (342.3, 257.0) & 2 & (187.9, 32.6) \\
3 & (63.1, 98.2) & 4 & (78.2, 195.3) \\
5 & (116.1, 35.4) & 6 & (234.5, 141.8) \\
7 & (223.4, 142.3) & 8 & (275.4, 163.7) \\....... &....... &....... &....... \\
33 & (356.9, 25.5) & 34 & (162.7, 241.0) \\
35 & (248.3, 178.1) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Co-ordinates of cluster centers for busy periods. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Date** & **13 th** & **14 th** & **15 th** & **16 th** & **17 th** & **18 th** & **19 th** \\ \hline Number of clustering centers & & & & & & \\ during busy periods & & & & & & \\ \hline Number of clustering centers & & & & & & \\ for idle time segments & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Number of clustering centers for 7-day busy/idle periods. 0.654, 0.523, 0.625] to the current {0.517, 0.593, 0.548, 0.601}, and the standard deviation of the integrated network index of each sector has been reduced by 51.2% compared with that of the original sector. After the designation of sectors, the fluctuation of comprehensive network indicators is smaller, the distribution is more balanced, and the flight situation in the sectors has better stability, which is convenient for controllers to maintain stable and efficient working condition. In order to further verify the rationality and effectiveness of the model proposed in this paper, the radar data of the 18:00-20:00 period (busy period) on the 14 th and the 07:00-09:00 period (idle period) on the 17 th are calculated. The average number of conflicts per unit time and sector before and after sector division is compared, and the results are shown in Figure 11.  
Figure 9: Final sectorization results. (**a**) Sectorization during busy hours; (**b**) Sectorization during idle hours. The graph shows that after the model is divided, the average number of conflicts per unit time and sector of each sector in the idle period is changed from \(\{7,3,5,1\}\) to \(\{5,4,4,3\}\), and the average number of conflicts per unit time and sector of each sector in the busy period is changed from \(\{10,6,11,8\}\) to \(\{9,7,10,9\}\). The average number of conflicts per unit  
Figure 11: The average number of conflicts per unit time and sector before and after delineation. (**a**) The average number of conflicts per unit time and sector during idle hours; (**b**) The average number of conflicts per unit time and sector during busy hours. Figure 10: Comparison of network data before and after delineation. (**a**) Comprehensive network metrics during busy hours; (**b**) Comprehensive network metrics during idle hours; (**c**) Standard deviation of comprehensive network metrics during busy hours; (**d**) Standard deviation of comprehensive network metrics during idle hours. time and sector can reflect the size of the control load to a certain extent.