# A Geographical Heuristic Routing Protocol for VANETs
## 5 Performance Evaluation
### Evaluation of the Recovery Phase in GHR
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metric** & **Number of Density** & **Forwarding Factor** & **Wilk’s \(\Lambda\)** & **F (2,18)** & \(p\)**-Value** \\ \hline \multirow{4}{*}{\% of Packet Losses} & 100 & \(\infty\) \& 3 & 0.357 & 16.210 & 0.0001 \\  & 150 & \(\infty\) & 0.662 & 4.592 & 0.024 \\ \multirow{2}{*}{\% of Packet Losses} & 150 & 3 & 0.679 & 4.261 & 0.031 \\  & **250** & \(\infty\) & **0.894** & **1.067** & **0.365** \\  & 250 & 3 & 0.427 & 12.076 & 0.001 \\ \hline \multirow{4}{*}{Average delay} & 100 & \(\infty\) \& 3 & 0.204 & 35.17 & 0.0001 \\  & 150 & \(\infty\) \& 3 & 0.169 & 44.11 & 0.0001 \\ \multirow{2}{*}{Average number of hops} & 250 & \(\infty\) & 0.167 & 44.99 & 0.0001 \\  & 250 & 3 & 0.65 & 129.924 & 0.0001 \\ \hline \multirow{4}{*}{Average number of hops} & 100 & \(\infty\) \& 3 & 0.217 & 32.486 & 0.0001 \\  & 150 & \(\infty\) & 0.198 & 36.398 & 0.0001 \\ \multirow{2}{*}{Average number of hops} & 150 & 3 & 0.081 & 63.96 & 0.0005 \\  & 250 & \(\infty\) \& 3 & 0.241 & 28.373 & 0.0005 \\ \hline \multirow{4}{*}{\% of idle time} & 100 & \(\infty\) \& 3 & 0.110 & 72.73 & 0.0001 \\  & 150 & \(\infty\) \& 3 & 0.219 & 32.05 & 0.0001 \\ \multirow{2}{*}{\% of idle time} & 250 & \(\infty\) & 0.234 & 29.478 & 0.0001 \\  & 250 & 3 & 0.493 & 9.251 & 0.002 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: MANOVA [37] results of the testing difference in performance metrics among routing recovery techniques (\(RT\)). There is a significant difference when the \(p\)-value \(<\) 0.05. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of Vehicles** & **Performance Metric** & **Wilk’s \(\Lambda\)** & **F (2,18)** & \(p\)**-Value** \\ \hline \multirow{4}{*}{150} & All metrics together * & 0.358 & 1.784 & 0.06 \\ \cline{2-5}  & All metrics together * & 0.228 & 5.07 & 0.006 \\  & **\% of packet losses** & **0.658** & **4.771** & **0.022** \\ \multirow{4}{*}{150} & Average delay & 0.907 & 0.919 & 0.095 \\  & **Average No. of hops** & **0.514** & **8.51** & **0.003** \\  & **\%** of idle time & 0.761 & 3.866 & 0.055 \\ \hline \multirow{4}{*}{250} & All metrics together * & 0.334 & 2.996 & 0.043 \\  & **\% of packet losses** & **0.706** & **3.05** & **0.041** \\ \cline{1-1}  & **Average delay** & **0.548** & **7.415** & **0.004** \\ \multirow{2}{*}{\% of hops} & Average No. of hops & 0.798 & 2.275 & 0.202 \\ \cline{1-1}  & **\% of idle time** & **0.508** & **8.718** & **0.002** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: MANOVA [37] results for the interaction test among recovery techniques (\(RT\)) and the forwarding technique (\(FT\)) for the recovery phase of GHR. * Degrees of freedom in the F statistic are 8 and 12. If there is a significant interaction (\(p\)-value \(<\) 0.05) in the “all metrics together” test, then interaction tests per metric need to be performed. Table 7 shows the results of the pairwise comparisons among the recovery techniques (i.e., (\(\beta\rightarrow\infty\), \(\beta=3\)), (\(\beta\rightarrow\infty\), \(\beta=0\)), (\(\beta=3\), \(\beta=0\))) following Step 3 of the analysis, in which differences between \(\beta\) values are not statistical significant for a particular metric (i.e., \(p\)-value \(\geq 0.05\)). In these cases, the average values of the metrics are very similar and can be considered statistically the same. The rest of the results of the pairwise comparison tests, e.g., the average end-to-end delay in the three vehicle densities, obtained \(p\)-values \(<\)0.05, and we do not include them in Table 4. Those \(p\)-values indicate that the value of the recovery factor \(\beta\) has an impact on the values of the metrics. The comparisons of average values of the four performance metrics with the different forwarding techniques are depicted in Figure 6.