# A Geographical Heuristic Routing Protocol for VANETs
## 5 Performance Evaluation
### Evaluation of the Forwarding Phase in GHR  
To evaluate the forwarding phase of our Geographical Heuristic Routing (GHR) protocol, we distinguish three factors that could affect the performance of the GHR. These factors are:  
1. The vehicle density of the scenario (\(VD\)). 2. The use of a Tabu list in the routing (\(T\)). 3. The forwarding technique (\(FT\)). We compare the four different ways that GHR uses to select the next forwarding node: the best legal neighbor (\(\alpha\rightarrow\infty\)), a random legal neighbor (\(\alpha=0\)), randomly according to Simulated Annealing (SA) (\(\alpha=3\)) or the use of the first legal neighbor. Following the three-step procedure described in previous Section 5.2, we have to analyze the results for each density separately because there is a significant three-way interaction \(FT\times T\times VD\) (Step 1) with a \(p\)-value = 0.001 (Wilk's \(\Lambda\) = 0.377 and F (24,92) = 2.41). Table 2 shows the results of the further interaction test between the use of Tabu \(T\) and \(FT\) for the GHR protocol (Step 1). First, we perform the so-called \"all together\" test in which we evaluate the interaction between the two factors considering the correlation among the six performance metrics. If the \(p\)-value \(<\) 0.05 for this test, we further carry separate interaction tests for each metric. In Table 2, we can see that for the medium and the high density scenarios, the \"all together\" test has a \(p\)-value under the threshold, so independent interaction tests per metric need to be performed in those cases. The results of the interaction tests for each metric indicate that the seeking of performance differences in the forwarding technique has to differentiate if tabu were used or not in the routing in the medium and high density scenarios (150 and 250 vehicles, respectively) to compare the average number of hops. There is also this significant interaction (i.e., \(FT\times T\)) for the evaluation of the percentage of idle time in the scenario of 250 nodes. The test results to determine if there are differences in the performance metrics, according to Step 2 of the statistical procedure of Section 5.2, are shown in Table 3. For this analysis, the data of the metrics were grouped according to the results of the interaction tests analyzed previously. This means that in most of the cases, we performed only one test per metric in each density without differentiating \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of Vehicles** & **Performance Metric** & **Wilk’s \(\Lambda\)** & **F (3,17)** & \(p\)**-Value** \\ \hline
100 & All metrics together * & 0.284 & 1.684 & 0.234 \\ \hline  & All metrics together * & 0.103 & 5.834 & 0.009 \\  & \% of packet losses & 0.858 & 0.941 & 0.442 \\
150 & Average delay & 0.661 & 2.910 & 0.065 \\  & **Average No. of hops** & **0.335** & **11.272** & **0.0001** \\  & \% of idle time & 0.666 & 2.840 & 0.069 \\ \hline  & All metrics together * & 0.113 & 5.235 & 0.013 \\  & **\% of packet losses** & **0.502** & **0.284** & **0.007** \\
250 & Average delay & 0.665 & 2.858 & 0.068 \\  & **Average No. of hops** & **0.369** & **9.691** & **0.001** \\  & **\% of idle time** & **0.549** & **4.653** & **0.015** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: MANOVA [37] results for the interaction test between the forwarding technique (\(FT\)) and the use of Tabu (\(T\)) for the forwarding phase of GHR. * The degrees of freedom in the F statistic are 12 and 8. 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. whether Tabu is enabled during the simulation. We labeled these cases as \"together\" in the Tabu column. All of the \(p\)-values in this table are lower than 0.05, excluding the percentage of packet losses in the medium density scenario (150 vehicles) and the average end-to-end delay for the three vehicle densities.