## 4 Simulations and Results
### Simulation Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Performance** \\ **Metric** \\ \end{tabular} } & \multirow{2}{*}{**Pairwise**} & \multirow{2}{*}{\begin{tabular}{c} **Standardized** \\ **Test Statistic** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} _p-Value** \\ **2 Sides** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Is the Difference** \\ **Significant** \\ **(\(p\)-Value \(<\) 0.017)?** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Median of** \\ **Differences** \\ \end{tabular} } \\ \hline \multirow{4}{*}{Packet losses} & Realistic, total block & 2.983 & 0.003 & Yes & \(-\)2.3780\% \\  & Realistic, pre-computed & 3.602 & 0.0001 & Yes & \(-\)3.0614\% \\  & Total block, pre-computed & 1.423 & 0.155 & No & \(-\)0.91\% \\ \hline \multirow{4}{*}{Average delay} & Realistic, total block & 4.019 & 0.0001 & Yes & \(-\)0.5310 s \\  & Realistic, pre-computed & 3.360 & 0.001 & Yes & \(-\)0.4391 s \\  & Total block, pre-computed & -0.565 & 0.572 & No & 0.0136 s \\ \hline \multirow{2}{*}{Average number of hops} & Realistic, total block & \(-\)5.309 & 0.0001 & Yes & 0.66 hops \\  & Realistic, pre-computed & 1.559 & 0.119 & No & \(-\)0.11 hops \\  & Total block, pre-computed & 5.242 & 0.0001 & Yes & \(-\)0.78 hops \\ \hline \multirow{2}{*}{Average number of neighbors} & Realistic, total block & \(-\)2.091 & 0.037 & No & 0.285 nodes \\  & Realistic, pre-computed & \(-\)2.599 & 0.009 & Yes & 0.485 nodes \\  & Total block, pre-computed & \(-\)0.153 & 0.878 & No & \(-\)0.075 nodes \\ \hline \multirow{2}{*}{Average number of neighbors} & Realistic, total block & \(-\)0.816 & 0.415 & No & 0.06 nodes \\  & Realistic, pre-computed & 1.734 & 0.83 & No & \(-\)0.315 nodes \\  & Total block, pre-computed & 2.499 & 0.012 & Yes & \(-\)0.565 nodes \\ \hline \multirow{2}{*}{Average number of neighbors} & Realistic, total block & \(-\)2.803 & 0.005 & Yes & 0.39 nodes \\  & Realistic, pre-computed & 1.020 & 0.308 & No & \(-\)0.185 nodes \\  & Total block, pre-computed & 2.497 & 0.013 & Yes & \(-\)0.525 nodes \\ \hline \hline \end{tabular}
\end{table} 
Table 4: \(p\)-Values of Wilcoxon signed rank test for a pairwise comparison of the building attenuation model effect. (**a**) Barcelona scenario. 1 AP. Uniformly distributed traffic; (**b**) Tarragona scenario 6 APs. Exponentially distributed traffic. the total absence of communication, compared with the results obtained with a realistic channel model, specifically designed for VANETs. Comparison between these two models in the Tarragona scenario shows significant differences in the average number of hops (see the fourth row in Table 4b). Moreover, the total signal blocking always shows the most conservative behavior. This can be noticed in the values of the column of the median of the differences in both Table 4a and 4b). This behavior makes total sense, since this model involves nodes sensing fewer neighbors (vehicles cannot detect nodes behind obstacles in any case under the total-blockage attenuation model). Additionally, the absence of communications avoids the construction of paths that in a realistic approach may be feasible. Consequently, packets need to be stored in nodes for longer periods until finding a forwarding node, so the percentage of packet losses increases due to the timeouts. Notice that in the Barcelona scenario, the differences in the average number of neighbors are only detected in the high density case. This behavior is explained by the communications between obstructed nodes not being the rule, and most of them entail high error probabilities. As a consequence, the differences in the performance metrics are small in our simulations scenarios, as is shown in the column of the reported medians. Regarding the comparison between the realistic channel model and the pre-computed attenuation approach, it can be noticed (see Rows 8, 14 and 17 in Table 4a) that there is no statistically significant difference in the average number of hops or neighbors.