# Onboard Centralized ISL-Building Planning for LEO Satellite Constellation Networks
## 5 Performance Evaluation
### Influence of Different Value of Time Segment Length  
As mentioned in the previous sections, in some works, FSA has been used to describe the ISL-building planning problem in one period [11; 15; 16]. The system period is divided into several equal-length time segments, and a fixed network topology is maintained in each time segment. The ISLs visible at each time in the time segment are considered to be visible in the time segment. Generally speaking, in the process of visibility calculation, the start and end time points of the visible time segments are not aligned with the equal-length time segments of the FSA. If the time segment length is too large, some visible time segments that could have been used to build ISLs would be wasted, resulting in a reduction in the number of ISLs and, consequently, degradation of the network topology performance. However, on the other hand, if the time segment length is too small, the whole network topology may switch frequently, also reducing the network performance. Therefore, selecting an appropriate time segment length is important, which can allow for a reduction of the network topology switching frequency without increasing the network delay. Another way to process the time segment of FSA is not to use an equal-length time segment; that is, the calculated visible time segments are used to build ISLs without alignment to the equal-length time segments. In a system with a time accuracy of one second, not using an equal-length time segment is equivalent to the equal-length time segment with a length of one second. \begin{table}
\begin{tabular}{c c c} \hline \hline Semi-Major Axis & 8500 km \\ \hline Eccentricity & 0.0000 \\ \hline Inclination & 60\({}^{\circ}\) \\ \hline Longitude of the ascending node & 0\({}^{\circ}\) \\ \hline Argument of periapsis & 0\({}^{\circ}\) \\ \hline Mean anomaly at epoch & 0\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Orbital elements of the seed satellite in Walker Delta 32/4/1 constellation. \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Azimuth** & **Elevation** & **Half-Angle** \\ \hline ISL Terminal I & 0\({}^{\circ}\) & 0\({}^{\circ}\) & 89\({}^{\circ}\) \\ \hline ISL Terminal II & 180\({}^{\circ}\) & 0\({}^{\circ}\) & 89\({}^{\circ}\) \\ \hline ISL Terminal III & \(-\)90\({}^{\circ}\) & 0\({}^{\circ}\) & 89\({}^{\circ}\) \\ \hline ISL Terminal IV & 90\({}^{\circ}\) & 0\({}^{\circ}\) & 89\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The installation direction and turntable rotation half-angle of each ISL terminal. In order to select the appropriate time segment length in FSA for the method proposed in this paper, in this subsection, we compared the implementation results of the method under different time segment lengths. Common time segment lengths are 300 s or 600 s [11; 16]. In the simulation, the time segment length was set to 150 s (LPTSO-150s), 300 s (LPTSO-300s), 450 s (LPTSO-450s), 600 s (LPTSO-600s), 750 s (LPTSO-750s), and an unequal-length time segment (LPTSO-1s). In the Walker Delta 32/4/1 constellation, based on the various different time segment lengths, the method proposed in this paper was implemented, and the network topology performance metrics such as ISL duration, topology duration, average delay, and maximum delay, were compared. Figure 5 shows the experimental results for average ISL duration and average topology duration under different time segment lengths. We can see, from the figure, that when the time segment was less than or equal to 300 s, the average ISL duration and the average topology duration were almost consistent. When the time segment length was greater than 300 s, with an increase in the time segment length, the average ISL duration decreases while the average topology duration increased.