## 7 Numerical Results
### Results
After having validated the GSESH algorithm, we apply it to a complete orbital scenario to evaluate how the possibility to process data on board of satellites and to leverage the full constellation in processing in such a way that if a satellite does not have enough resource to process data can offload the elaboration to another satellite, allows to save energy on the GS. In Figure 7, we report the ground station energy saving as a function of the maximum number \(\alpha\) of tasks that can be processed by a satellite during a time cycle, for \(\alpha\in[0,\ldots,50]\), and \(\
abla=1\%\) (i.e., \(\varepsilon_{Sat}/\tau=17\) W, or, equivalently, \(\varepsilon_{Sat}=10,200\) J). We report the results of the following solutions: GSESH represents the proposed heuristic, FoG involves task processing being allowed only on the satellite which acquired the image or on the ground, while in the AG solution, data can be only elaborated on the ground. In order to better understand the energy-saving trends related to the GSESH solution, we also report the following energy-consumption components as a function of the time cycle: the energy consumed by the GSs in Figure 8; the total (processing and transmission) energy used by satellite 13 of the considered a constellation in Figure 9; the space segment total energy consumption (i.e., the sum of the total energy consumption of all the satellites in the constellation) in Figure 10. In each figure, three curves are reported for values \(\alpha\) equal to 5, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 3  
and 20, corresponding to \(\alpha\) values smaller than, equal to, and higher than the optimum value \(\alpha=12\) showing the maximum ground station energy saving, as can be noticed in Figure 7.  
The results reported in Figure 7 show that when there is the possibility to process data on board (i.e., in case of the GSESH algorithm or FoG benchmark solution), we save energy on GSs, and the ground station energy-saving trend follows the same behaviour as discussed before. In particular, the peak energy saving in ground stations is reached for an increased value of \(\alpha\) with respect to the case seen for the heuristic validation, since in this case we have an increased amount of energy available on board (in particular, \(\
abla=1\%\) with respect of \(\
abla=0.1\%\) of the previous analysis) to handle a higher number of services. Furthermore, in this complete case-study orbital scenario, it is possible to notice that in the region where ground station energy saving decreases because of limited on-board energy, there are some \(\alpha\) value regions where the energy saving remains constant. This is because of the energy margin limiting the amount of data each satellite can handle. Finally, as expected, energy saving in the ground station is zero when the AG benchmark solution is applied. The ground station energy-saving trend is confirmed by the results shown in Figures 8-10, where we can remark that: (i) the energy consumption on the GSs (Figure 8) is minimum when the processing capacity installed on board satellites is such that \(\alpha=12\) (Figure 8b), i.e., for the \(\alpha\) value associated to maximum energy saving on ground, while higher consumption is reached for \(\alpha\) equal to 5 (Figure 8a) and 20 (Figure 8c), i.e., when satellites have limited processing capacity or in case the energy required to process all the images each satellite would be able to elaborate on board is higher than the energy available on board, respectively; (ii) both the total energy consumption on any satellite, i.e., satellite 13, (Figure 9) and the total energy consumption of the space segment (Figure 10) are minimum for \(\alpha=5\) because satellites are able to process only a few (at most 5) tasks in a time cycle, while they are both maximum for \(\alpha=20\).