## 4 Simulations and Results
### Simulation Results  
In this section, we present some results from comparing the simulations of the three aforementioned attenuation models: realistic, total blockage of signal and pre-computed attenuation. The evaluation is focused on four widely-used metrics applied to the performance analysis of VANET routing protocols. These metrics are the percentage of packet losses, average delay, average number of hops and average number of neighbors. Figures 8 and 9 illustrate these results for the four node densities in the two scenarios. The mixed ANOVA statistical test [21] was employed to check if the performance metrics differences among attenuation models depends on the vehicle density in the evaluated area. There might be a relationship since a great number of nodes may generate more collisions and higher levels of interference. We use mixed ANOVA, because for each vehicle density, the same ten vehicle movements were used to test the attenuation models. For mixed ANOVA, our data are organized into twelve groups that are obtained by combining the three building attenuation models with the four vehicle densities in the simulation. All groups have the same number of elements, which allows one to have a balanced test. The outcome of the statistical test is a probability called the \(p\)-value, which is \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & \multicolumn{2}{c}{**Value**} \\ \hline
**Map Zone** & **Example District of Barcelona** & **Downtown of Tarragona** \\ Area & 1.5 km \(\times\) 1 km & 1.6 km \(\times\) 1.3 km \\ Number of junctions & 712 (475 \(\times\) km\({}^{2}\)) & 783 (373 \(\times\) km\({}^{2}\)) \\ Number of streets (edges) & 920 (613 \(\times\) km\({}^{2}\)) & 993 (472 \(\times\) km\({}^{2}\)) \\ Number of buildings (polygons) & 2216 (1477 \(\times\) km\({}^{2}\)) & 720 (346 \(\times\) km\({}^{2}\)) \\ Number of nodes & 100, 150, 200 and 250 vehicles & 133, 200, 266 and 333 vehicles \\ Inter-packet generation time & t\(\sim\)U(2,6) s E(t) = 4 s & t\(\sim\)Exp(mean = 4, min = 1, max = 10) s \\ Maximum packet size & & 1000 bytes \\ Path loss model & Empirical model of IEEE 802.11p radio shadowing [5] \\  & \(\bullet\) Realistic [5]\(\alpha=9 db/wall\)\(\beta=0.4 db/m\) \\ Building models & \(\bullet\) Total block of signal \\  & \(\bullet\) Pre-computed attenuation (Figure 5b) \(Step=3\) \\ Fading model & Ricean (LOS) and Rayleigh (not in LOS) \\ Power transmission & 23 dbm \\ Receiving sensing & \(-82\) dbm (\(\sim\) 400 m in LOS) \\ Mobility generator & SUMO [20] / C4R [19] \\ MAC specification & IEEE 802.11p \\ Bandwidth & 6 Mbps \\ Simulation time & 300 s \\ Routing protocol & MMMR [11] \\ GPS precision & 10 m \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation settings. named the significance level. If the _p_-value is lower than the significance level, then the performance results of the system are related to both the attenuation model and the vehicle density. The _p_-values, which we obtained from checking the dependency between the attenuation model and the vehicle density, are depicted in Table 2, where the F-ratio is the result of the F-test statistical test [22], df represents the degrees of freedom used to obtain the _p_-value and partial \(\eta^{2}\) is a measure of the effect size. According to the results of the Mixed-ANOVA, we can conclude that there is no  
Figure 8: Building attenuation model comparison (Barcelona scenario) (CI 95%). (**a**) Percentage of packet losses; (**b**) average end-to-end delay; (**c**) average number of hops; (**d**) average number of neighbors. Figure 9: Building attenuation models comparison (Tarragona scenario) (CI 95%). (**a**) Percentage of packet losses; (**b**) average end-to-end delay; (**c**) average number of hops; (**d**) average number of neighbors. significant interaction between the attenuation models and the vehicle density, since the _p_-value is lower than 0.05 in none of the performance metrics for both scenarios, except for the average number of neighbors.