# Autonomous Controller-Aware Scheduling of Intra-Platoon V2V Communications
## 6 Numerical Results
The reason for such an observation may be the fact that a long-term differences in periodicity used for different platoon vehicles may result in the loss of string stability, thus leading to safety degradation. Thus, there is no justification for the use of hysteresis, as it results in higher resources consumption at no improvement (or even degradation) of safety. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of platoon vehicles & 6 \\ \hline Inter-vehicle spacing in platoon (\(d_{d}\)) & 3 m \\ \hline Intra-platoon message periodicity (\(T_{d}\)) & [20, 50, 100, 200, 500, 1000] ms \\ \hline Simulation time step & 1 ms \\ \hline Maximum acceleration (\(a_{\text{max}}\)) & 4 m/s\({}^{2}\) \\ \hline Minimum acceleration (\(a_{\text{min}}\)) & \(-\)4 m/s\({}^{2}\) \\ \hline Maximum velocity & 30 m/s \\ \hline Maximum leader acceleration disturbance (\(z_{\text{max}}\)) & 3 m/s\({}^{2}\) \\ \hline Minimum leader acceleration disturbance (\(z_{\text{min}}\)) & \(-\)3 m/s\({}^{2}\) \\ \hline Leader acceleration disturbance mean inter-arrival time & [5,10,15,20,25] s \\ \hline Platoon controller constants (\(\{\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{4},\alpha_{5}\}\)) & \(\{-\)0.04, \(-\)0.3, \(-\)0.1, 0.5, 0.5\}\) \\ \hline Heuristic algorithm prediction time span (\(t_{\text{Th}}\)) & 50 s \\ \hline Heuristic algorithm hysteresis memory size (\(r\)) & [0, 200, 500, 1000] ms \\ \hline Emergency braking activation distance (\(d_{\text{Th}}\)) & 1 m \\ \hline Number of simulation runs per point & 50 \\ \hline Single simulation run duration & 700 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. The observations from Figure 7 are confirmed with the analysis of the distance error evolution in a selected single simulation run. Figures 8 and 9 show examples of such an evolution for a configuration with a fixed interval of 500 ms, and for the adaptive approach with no memory (no hysteresis), respectively. One can notice in Figure 8 that the fixed interval approach using moderate resources consumption may result in the activation of emergency braking when a series of acceleration changes occurs, leading to an increase in the distance error between the leader vehicle and the first follower over the threshold value of 2 m. In the example run presented in Figure 8, five such occurrences can be observed for the first platoon pair (between the leader and the first follower), corresponding to approximately 3.4% of the total simulation time. The other platoon vehicles manage to keep a much smaller distance error, with the maximum value only slightly exceeding 1 m, as with the fixed interval approach, the string stability of the platoon in ensured, and so for each next vehicles' pair, the error is becoming smaller. The situation is slightly different  
Figure 6: Total number of intra-platoon transmissions per simulation run (700 s) vs. selected transmission period and mean inter-arrival of \(z_{0}\) random variable. Figure 7: Fraction of emergency braking distance violations per simulation run (700 s) vs. selected transmission period and mean inter-arrival of \(z_{0}\) random variable. when the adaptive approach is used, as shown in Figure 9. Here we observe no distance error threshold violations, with the maximum inter-vehicle distance of approximately 1.9 m being observed for the first pair in the platoon, and so emergency braking is never activated. On the other hand, the distance error for vehicles' pairs that are located closer to the platoon tail may actually exceed in certain situations the distance error observed for the leader-first follower pair. Such observations can be made in Figure 9 in two time regions when accounting for the positive distance error, around 32 s and 525 s, with the maxima of approximately 1.52 m and 1.42 m being noted for the distance between vehicles 3 and 4.