## 5 Performance Evaluation
### Results and Discussion
#### 5.2.1 Impact of Vehicle Density  
The density of vehicles always plays a vital role in the evaluation of any proposed algorithm in a connected vehicular environment. As more and more vehicles are connected to the network, the vehicle density can either increase the performance of a certain algorithm with its increase or decrease the performance with increasing density. The algorithms are evaluated with three different densities of vehicles, i.e., low, medium, and high. The low density consists of 30-50 vehicles/km, the medium density consists of 51-80 vehicles/km and the high density consists of 81-125 vehicles/km.  
All three algorithms were evaluated in the respective attack scenarios, and each algorithm performed very well when the density of the connected vehicles was kept low, as shown in Table 4. They showed even better performance in Attack Type 3, which is a little harder to detect as compared to the first two attack types.  
The respective algorithms were evaluated in the medium vehicle density to inspect the accuracy rate of each algorithm, as shown in Table 5. It was observed that the algorithms performed well when it came to the first two attack scenarios; however, there was a slight decrease in the accuracy rate regarding the Attack Type 3 scenario as the attacker vehicle pretended to be a legitimate vehicle for some time before initiating the position falsification attack.  
Lastly, the accuracy rate of the algorithms was evaluated in the high density of connected vehicles ranging from 81-125 vehicles/km as shown in Table 6. The first two attack scenarios were accurately detected by multi-BSM and vouch scheme; however, [PERSON] et al. showed a little decrease in the accuracy rate of Attack Type 2. All the three compared algorithms showed a decrease in accuracy rate regarding Attack Type 3, with [PERSON] et al. being the lowest in comparison to the other two algorithms.  
Figure 5 shows the correlation between energy consumption and vehicle density in the increasing order at the RSU. It can be seen that the vouch algorithm consumes the most energy as the density of the vehicles is increased. The multi-BSM and Grover algorithms are somewhat similar in consumption of the energy, with the multi-BSM being a bit higher.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Attack Type 1** & **Attack Type 2** & **Attack Type 3** \\ \hline [PERSON] et al. [13] & 100 & 98 & 94.9 \\ Vouch [24] & 100 & 100 & 96.3 \\ Multi-BSM & 100 & 100 & 97 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of accuracy rate in high vehicle density.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Attack Type 1** & **Attack Type 2** & **Attack Type 3** \\ \hline [PERSON] et al. [13] & 100 & 100 & 100 \\ Vouch [24] & 100 & 100 & 100 \\ Multi-BSM & 100 & 100 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of accuracy rate in low vehicle density.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Attack Type 1** & **Attack Type 2** & **Attack Type 3** \\ \hline [PERSON] et al. [13] & 100 & 99 & 97.1 \\ Vouch [24] & 100 & 100 & 98.2 \\ Multi-BSM & 100 & 100 & 99 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of accuracy rate in medium vehicle density.