## 6 Results
### Lifetime Results
By looking at the feature rank and individual results that both the MIP and the GRASP deliver for the correct and the missed nodes, it can be clearly seen that such nodes share many similarities, their constant appearance in the critical node test set being the first and most important one. In the case of network #5, the missed and the correct critical nodes are within reach of the base station, with an extensive neighborhood. Regarding the relay feature, the MIP grants both nodes a very similar value, among the top ones, and the GRASP assigns the same relay value. Equal to the latency case mentioned before, the similarity in the final MIP lifetime value makes it difficult for the GRASP to properly find the optimal value. Network #7 shares many similarities with the aforementioned network #5. Equally, the missed and the correct critical nodes are in the range of the base station, and they both send data to it. Moreover, their neighborhood is among the top 10. Moreover, the MIP relay values are almost identical between the two nodes, being identical in the case of the GRASP. Final lifetime values only differ by a single unit in the case of the MIP. For such reason, it is very difficult for the GRASP to reach the optimal scenario. In conclusion, even though the success rate for the first critical node is not 100%, it can be seen that the missed cases can also be useful for understanding the characteristics of the network and the critical nodes. Figure 4(a) shows the results for the tests in which node density is increased. Each of the lines A-\(C\) shows the average impact when removing the most \(C\) critical nodes from the network. As it can be seen, the behavior of the previous average latency increase results and the current average lifetime decrease share many similarities. Firstly, as the number of nodes inside the network increases, the degradation in the lifetime lowers, mainly due to the flexibility that dense networks offer in terms of available paths for distributing the data delivery. Second, and most importantly, it can be seen that, if nodes inside the network share the same battery capacity, the lifetime decreases as the number of critical nodes removed increases. When a critical node \(n\) is removed, the network slightly loses flexibility, and paths crossing \(n\) need to be redirected to a more costly destination, reducing the lifetime of those nodes and thus the overall network lifetime. Figure 4(b) extends the previous results by showing, in this case, the maximum lifetime decrease values obtained. It is worth noticing that, although the decreasing tendency is slightly maintained, the smoothness of the curve previously seen disappears. Again, these results are only representative of the network space tested, and the study of different network layouts may vary the maximum results. However, it is not possible to study every single network due to the amount of possibilities. Average and maximum execution times are respectively shown in Figure 5c,d. Both plots show the exact same exponential tendency. However, maximum values are much higher, arriving to double the average in some cases. Results for lifetime in scaled networks are presented in Figure 6. Similar to the latency model, the horizontal tendency appears as shown in Figure 6a. However, in this case, the variations between different network sizes are more considerable, but it can be concluded that the lifetime decrease is maintained when the network is scaled up. Nonetheless, when looking at the maximum decrease values in Figure 6b, instead of a horizontal tendency, a slight increase is seen. Figure 5d shows the average execution time for the lifetime decrease model. The exponential tendency is clearly seen for the AV-2, AV-3 and AV-4 cases. Equally, in the case of maximum execution times depicted in Figure 6d, this exponential tendency continues but with bigger time values, arriving to more than 2 h in some cases. Figure 5: Average and maximum lifetime decrease values and execution times for networks with nodes distributed in a 200 m radius area.