## 4 Mobility Model, Performance Comparison and Discussion
In Figure 4, the \(sd\) as a function of the vehicles velocity in a platooning scenario is demonstrated. The safety distance is mainly affected by the reaction time of the second vehicle. The human reaction time is equal to 1.37 s [34], while with the RF or VLC communication system the reaction time is the latency time to receive the alert message correctly from the other vehicle, which activates the automated braking system. To define the latency of the RF technologies for vehicular communications, the experimental results in [8] was used. In particular, the latencies results:  
* 50 ms for IEEE802.11p standard;
* 40 ms in C-V2X based on LTE network;
* 10 ms in C-V2X based on 5G network. For the VLC communication system, we considered \(\mathrm{SAL}=2.5\,\mathrm{ms}\), as this value is granted with probability \(>99.95\%\) for distances up to 9 m (see Figure 3a,c). As it can be observed in Figure 4, the safety distance between two vehicles (even with speed equal to 120 km/h) equipped with a VLC communication system could ideally be reduced to less than 0.1 m even in highway speed conditions. The results of Figure 4 has been summarized in Table 2. The minimum safety distance significantly decreases with the VLC communication technology compared to others. Although safety distances are very small also for RF technologies, the VLC system provides one magnitude less. The same mobility model is used to evaluate the performance of the proposed VLC system for two vehicles with different initial velocity. In this case, the two vehicles are assumed not to be connected yet. As it can be derived from Figure 3a, the VLC system experiences high error rate as the distance increases. Thus, if the safety distance of the vehicles is more than 15 m, vehicles cannot setup a connection, i.e., the safety distance has been calculated for every latency value (2.5, 5.6, 8.8, 11.9 and 15.1 ms) and if the safety distance is more than the distance in which the latency is ensured (see Figure 3a), the VLC communication between vehicles cannot be ensured with probability > 99.95%. The maximum difference between speeds that allows the connection between vehicles, and thus ensures braking, has been evaluated and the results are shown in Figure 5. The red zone in Figure 5 means that the value of the speed of the first vehicle and the value of the speed of the second vehicle do not guarantee the connection between the vehicles. For example, if the first vehicle has a speed of 60 km/h (\(x\)-axis in Figure 5), the speed of the second vehicle should not differ more than 10 km/h (\(y\)-axis in Figure 5) to setup a bidirectional connection by means of VLC signals. Figure 5 tells us also that if the first vehicle has high speed (120 km/h) the second one should have about the same speed to connect, and anyway with \"high\" latency (\(\approx\)15 ms). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Vehicles**} & \multicolumn{5}{c}{**Safety Distance [m] for Platooning Scenario**} \\ \cline{2-6}  & **VLC** & **5G** & **LTE** & **IEEE 802.11p** & **Human Reaction Only** \\ \hline
40 km/h & 0.03 & 0.11 & 0.44 & 0.55 & 8.78 \\
60 km/h & 0.04 & 0.17 & 0.66 & 0.82 & 16.40 \\
80 km/h & 0.06 & 0.22 & 0.88 & 1.10 & 24.01 \\
100 km/h & 0.07 & 0.28 & 1.10 & 1.38 & 31.62 \\
120 km/h & 0.08 & 0.33 & 1.33 & 1.66 & 39.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Safety distance (m) for different vehicles speeds and communication technologies. Simulations are carried out with the mobility model (Section 4) in case of platooning. Figure 4: Minimum safe distance \(sd\) in platooning use case for different velocity of the two vehicles.