## 4 Mobility Model, Performance Comparison and Discussion  
In this section, a mobility model for the vehicles is provided and used to compare VLC and RF connection capabilities to enable fast braking automated systems. A platooning scenario is assumed to compare the braking capabilities of VLC- and RF-connected vehicles. The mobility model is important to compare latency performance of RF communication standards and the proposed VLC system and to evaluate the limits of VLC in typical vehicular applications. In particular, we focused on the platooning case in an urban scenario, where the high density of vehicles makes RF communication not reliable enough to assure high-safety performances [18], mostly due to channel interference. We considered two vehicles running over a road in a platooning situation. We aim to calculate the safety distance (the initial distance before the braking starts) which allows the vehicles to avoid collision. The latency of the communication link between vehicles is critical to start braking on-time and avoid collisions. Platooning in this case means that each vehicle is obligated to follow the previous vehicle, with no possibility to change line. This is a frequent situation, in particular in urban areas. We aim to find which is the safety distance that two consecutive vehicles have to maintain in order to avoid collisions in case  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**PER**} & \multicolumn{6}{c}{**Probability to Achieve a SAL Value**} \\ \cline{2-6}  & \(\leq\)**2.5 ms** & \(\leq\)**5.6 ms** & \(\leq\)**8.8 ms** & \(\leq\)**11.9 ms** & \(\leq\)**15.1 ms** \\ \hline \(10^{-4}\) & \(>\)99.95\% & & & & \\ \(10^{-3}\) & 99.9\% & \(>\)99.95\% & & & \\ \(10^{-  
the first one suddenly starts a critical braking. When many vehicles are involved, it is important that each vehicle is connected to the previous and the following ones since this is what impacts the collision. The implemented model simulates the dynamic trajectory of two vehicles during platooning. The model is used to define the minimum safety distance between the vehicles for different velocities of the vehicles. Different braking methods between the vehicles are compared: human reaction and automated/assisted braking systems based on communication technologies. The communication technologies that we considered are: RF standards such as 802.11p and C-V2X (LTE-based and 5G-based) and the proposed VLC system. The speed of the vehicles is assumed to be the same and both vehicles are assumed to be equipped with an automated braking system, activated by an alert message coming from the other vehicle. To obtain the dynamic model of the two vehicles' motion in the platooning scenario, we split the motion in two phases:  
**Phase 1. **: The first vehicle starts to brake and its velocity decreases following the equation of uniformly decelerated motion. In the meanwhile, the second vehicle continues to move following the equation of linear motion with constant speed. This step lasts until the automated braking system engages. **Phase 2. **: After the latency time of the communication system, the automated braking system engages and the second vehicle starts to brake following the equation of uniformly decelerated motion. The first vehicle continues to brake as in the previous point. The deceleration value \(a\) used in uniformly decelerated motion is linearly proportional to gravitational acceleration \(g\)  
\[a=-\mu\,g \tag{1}\]  
when \(\mu\) is the friction coefficient. The friction coefficient is usually 0.7 for a road in good condition. The safety distance (\(sd\)) was evaluated as the difference between the braking distances of the two vehicles. To assure that a collision between the two vehicles does not occur, we set the safety distance \(sd\) as  
\[sd=\max\{sd_{phase_{1}},\,sd_{phase_{2}}\} \tag{2}\]  
where \(sd_{phase_{1}}\) and \(sd_{phase_{2}}\) are the safe distances derived from Phase 1 and Phase 2 described above, respectively.