## 6 Results
### Lifetime Results  
Equal to the latency model, the comparison between the MIP model and the GRASP meta-heuristic for small networks of \(N=100\) nodes distributed in a 200 m radius area are firstly presented. These results allow us to appreciate the margin error that the GRASP presents. Moreover, it can be checked whether GRASP ensures a correct critical node identification. Table 9 shows such results. Each network is represented by two rows: the first one makes reference to the one critical node removal test, whilst the second one stands for the case where two critical nodes are removed. It is worth remembering that the MIP iteratively deletes the critical nodes, whilst the GRASP does it simultaneously. Table 9 shows the comparison between the MIP model and the GRASP results, as well as the critical nodes' identifiers. The lifetime values shown express, as previously explained, the _time slots_ the network can be maintained fully operative if every node generates and sends one packet in each of these _time slots_. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Lifetime Values**} & \multicolumn{4}{c}{**Critical Node Ids**} \\ \hline  & **MIP** & **GRASP** & **Gap** & **MIP** & **GRASP** & **Success Rate** \\ \hline \multirow{3}{*}{Network \#1} & 167,909 & 120,252 & 28.38\% & 53 & 53 & 100\% \\  & 145,844 & 99,595 & 31.71\% & 13 & 30, 53 & 50\% \\ \hline \multirow{3}{*}{Network \#2} & 85,027 & 75,414 & 11.33\% & 84 & (3, 15, 84, 60) & 100\% \\  & 85,027 & 75,414 & 11.33\% & 60 & 60, 84 & 100\% \\ \hline \multirow{3}{*}{Network \#3} & 88,353 & 75,414 & 14.64\% & 85 & 85 & 100\% \\  & 75,438 & 70,277 & 6.84\% & 25 & 55, 85 & 50\% \\ \hline \multirow{3}{*}{Network \#4} & 301,263 & 191,629 & 36.39\% & 57 & 57 & 100\% \\  & 272,910 & 154,411 & 43.42\% & 83 & 57, 87 & 50\% \\ \hline \multirow{3}{*}{Network \#5} & 348,441 & 283,650 & 18.59\% & 44 & 32 & 0\% \\  & 328,744 & 257,812 & 21.57\% & 87 & 32, 87 & 50\% \\ \hline \multirow{3}{*}{Network \#6} & 118,880 & 118,842 & 0.03\% & 32 & 32 & 100\% \\  & 88,353 & 74,129 & 16.1\% & 36 & 36, 89 & 50\% \\ \hline \multirow{3}{*}{Network \#7} & 220,426 & 196,592 & 10.81\% & 91 & 36 & 0\% \\  & 134,354 & 100,277 & 25.36\% & 36 & 36, 40 & 50\% \\ \hline \multirow{3}{*}{Network \#8} & 153,052 & 118,842 & 22.35\% & 16 & 16 & 100\% \\  & 121,982 & 88,053 & 27.81\% & 11 & 16, 98 & 50\% \\ \hline \multirow{3}{*}{Network \#9} & 220,427 & 154,411 & 29.94\% & 96 & 96 & 100\% \\  & 181,638 & 131,809 & 27.43\% & 97 & 38, 96 & 50\% \\ \hline \multirow{3}{*}{Network \#10} & 105,355 & 89,298 & 15.24\% & 100 & 100 & 100\% \\  & 97,318 & 89,298 & 8.24\% & 58 & 58, 100 & 100\% \\ \hline \multirow{3}{*}{Average} & & 18.76\% & & & 80\% \\  & & 21.97\% & & & 60\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison between MIP and GRASP lifetime models. Nodes between parenthesis are interchangeable since they offer the same result when being removed. In this case, the difference between the MIP and the GRASP substantially differs. Thanks to the exactness of the MIP, node transmissions are split between different nodes instead of sending all the data to a single one. However, due to the approximation behavior of GRASP, the split of the transmissions cannot be exactly performed. As it can be seen, GRASP lifetime is 18% less for the one critical node removal case, and it increases to around 22% for the two critical nodes one. Looking at the networks independently, it can be seen that, in some cases, GRASP almost reaches the best value given by the MIP model. Critical node identification also suffers a degradation compared to the latency model. When removing the most critical network node, success rate is lowered to 80%, mainly due to the efficient transmission split that MIP performs. In the case of two critical nodes removal, the difference in node removal procedure also lowers the success rate to 60%. Networks #5 and #7 have been further analyzed in order to understand why the first critical node is not correctly pinpointed.