# A Geographical Heuristic Routing Protocol for VANETs
## 5 Performance Evaluation
### Evaluation of the Forwarding Phase in GHR
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metric** & **Number of Density** & **Tabu** & **Pairwise** & \(p\)**-Value** \\ \hline \multirow{6}{*}{\% of packet losses} & 100 & together & (\(\alpha\rightarrow\infty\), \(\alpha=0\)) & 0.317 \\  & 100 & together & (\(\alpha\rightarrow\infty\), \(First\)) & 0.276 \\  & 100 & together & (\(\alpha=0\), \(First\)) & 0.579 \\  & 250 & Yes & (\(\alpha\rightarrow\infty\), \(\alpha=0\)) & 0.98 \\  & 250 & Yes & (\(\alpha\rightarrow\infty\), \(First\)) & 0.855 \\  & 250 & Yes & (\(\alpha=0\), \(First\)) & 0.741 \\ \hline \multirow{3}{*}{Average number of hops} & 100 & together & (\(\alpha=0\), \(First\)) & 0.584 \\  & 150 & Yes & (\(\alpha=0\), \(First\)) & 0.142 \\  & 250 & Yes & (\(\alpha=0\), \(First\)) & 0.05 \\ \hline \multirow{6}{*}{\% of idle time} & 100 & together & (\(\alpha\rightarrow\infty\), \(\alpha=0\)) & 0.121 \\  & 100 & together & (\(\alpha\rightarrow\infty\), \(First\)) & 0.09 \\ \cline{1-1}  & 100 & together & (\(\alpha=3\), \(\alpha=0\)) & 0.067 \\ \cline{1-1}  & 150 & together & (\(\alpha\rightarrow\infty\), \(\alpha=3\)) & 0.584 \\ \cline{1-1}  & 150 & together & (\(\alpha\rightarrow\infty\), \(\alpha=0\)) & 0.444 \\ \cline{1-1}  & 150 & together & (\(\alpha=3\), \(\alpha=0\)) & 0.820 \\ \cline{1-1}  & 250 & No & (\(\alpha\rightarrow\infty\), \(\alpha=0\)) & 0.096 \\ \cline{1-1}  & 250 & Yes & (\(\alpha\rightarrow\infty\), \(First\)) & 0.096 \\ \cline{1-1}  & 250 & Yes & (\(\alpha=3\), \(\alpha=0\)) & 0.724 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pairwise comparison of the performance metrics in which there is a difference among forwarding techniques for the GHR protocol (i.e., \(p\)-value \(<0.05\) in Table 3). The table only shows the results for metrics and pairs of forwarding techniques with the absence of statistically-significant differences (i.e., \(p\)-value \(\geq 0.05\)). “Together” means that it is not needed to differentiate whether Tabu was enabled or not to apply the test. collisions or link saturation, and on avoiding already visited nodes by using the Tabu list. The other three approaches (i.e., \(\alpha\rightarrow\infty\), \(\alpha=0\) and _First_) have statistically the same results thanks to the use of Tabu. As can be seen from Figure 4b, the delay among the four different techniques is the same regardless of the use of Tabu routing for the three vehicle densities. This was confirmed by our statistical analysis, whose results (\(p\)-values \(\geq\) 0.05) are shown in the average delay section of Table 3. From Figure 4c, we can realize that applying a forwarding factor \(\alpha<\infty\), the average number of hops increases as is expected because the randomness in the forwarding increases, as well. Therefore, the highest number of hops is always obtained by a complete random selection (\(\alpha=0\)), and the lowest hop count takes place for the best selection (\(\alpha=\infty\)). When Tabu is used or in a low vehicle density, the selection of the first legal node needs as many hops as a random selection (see the \(p\)-value \(\geq\)0.05 of the pairs (\(\alpha=0\), _First_) in the average number of hops in Table 3). The percentage of idle time depicted in Figure 4d depends on the forwarding mechanism. The selection of the first legal neighbor has a high percentage of idle time for the three densities. This reveals a better use of the available bandwidth of this forwarding mechanism in spite of the high number of hops that the _First_ strategy needs to operate. The reason is that the _First_ strategy prefers to use recent updated neighbors, which have the most stable links, and therefore, will have a higher number of successful transmissions at the first attempt than other approaches, like best node or random selection. In fact, this technique reaches the highest value for the medium density scenario (150 nodes), while the other techniques obtain \(p\)-values \(\geq\) 0.05 in the pairwise comparisons of idle time;  
Figure 4: Performance evaluation of the forwarding techniques (_FT_) included in our proposed GHR.