## 5 Numerical Results
### Traffic Load Distribution  
Figure 7 shows the overall throughput in (14) versus the satellite spacing \(s\) for different total channel loads \(G_{T}\), considering both the uniform and the non-uniform traffic  
Figure 5: Packet loss rate \(\mathcal{P}\) vs. channel load \(G\) for the case of \(K=2\) satellites. We fixed the erasure probability \(\varepsilon_{1}\) at the first satellite to a different value for each of the subfigures, and we consider a set of different erasure probabilities \(\varepsilon_{2}\) at the second satellite in each subfigure. Figure 6: Packet Loss Rate \(\mathcal{P}\) vs. channel load \(G\) for \(K=2\) satellites and different pairs of erasure probabilities \([\varepsilon_{1},\varepsilon_{2}]\), in the case of low channel load. load distributions in (11) and (13), respectively. As we can see, the non-uniform always outperformed the uniform distribution when the channel load was high, but the uniform distribution led to a larger throughput for all or several satellite spacings when the channel load was relatively low. The non-uniform distribution performed better in high channel loads because, as the traffic load increased, it ensured that the number of potential simultaneous transmissions was greater (less) in positions with greater (less) throughput. Uniform traffic load distribution became very competitive in the case of very low total traffic load, as in this case there was an excess of resources for attending such small load, which allows us to conclude that the uniform distribution limits the system's scalability. Figure 7 also shows that, for both uniform and non-uniform distributions, the topologies with greater spacing \(s\) between satellites tended to achieve better performances, since they could distribute the traffic load among a greater number of positions \(M\), thereby reducing the collision probability. On the other hand, in those concentrated topologies (where the satellites are very close to each other or even practically together) with large channel loads, the benefit of using non-uniform instead of uniform distribution is greater, since the number of positions where both satellites are visible is larger in these topologies, and therefore the influence of load allocation increases. All in all, since non-uniform and uniform load distribution are not the best option in every case, the proposed ITLD algorithm is able to leverage the benefits of both. Another look at the performance of the proposed intelligent traffic load distribution method proposed in Section 4, and detailed in Algorithm 1, is given in Figure 8, which shows the throughput versus the total channel load for different spacings between \(K=2\) satellites. Again, in the case of low channel load, the uniform distribution outperformed the non-uniform (except when both satellites are together), but with the increase of the channel load we had the opposite (for all satellite spacing considered), showing again the impact of choosing the best load distribution in each case. Moreover, we can see that in the case of smaller spacings between satellites, the advantage of non-uniform distribution tended to be greater. Once more, we can see the importance of the proposed ITLD method, which allocated the traffic load according to the system condition (total channel load, satellite spacing, and positions). Figure 7: Overall throughput achieved by uniform and non-uniform traffic load distributions versus the spacing \(s\) between \(K=2\) satellites, with total traffic load of \(G_{T}\in\{36,72,108,144\}\) packets per lap. Finally, Figure 9 shows the throughput versus the number of satellites in the constellation for a relatively high channel load and different spacings between consecutive satellites. The non-uniform load distribution clearly outperformed the uniform one for all satellite spacings, but this advantage decreased with the number of satellites.