## 4 Performance Evaluation  
The performance of the proposed and ID models is evaluated on a 1 km circular road for 200 s using the Euler technique [53]. The proposed model is evaluated for a platoon of 40 CAVs with time headway 1 s, jam spacing 1.5 m [58], and reaction time 0.1 s [55]. The ID model is evaluated for a platoon of 36 vehicles with time headway 2 s [59] and jam spacing 2 m [32] so the platoons have the same length. The number of vehicles on the road was obtained by dividing the road length by the equilibrium distance headway \(S_{e}\). The value of \(S/S^{\prime}\) ranges between 0 and 1, so here 0.2, 0.5, and 0.8 are used. \(\delta\) varies between 1 and \(\infty\) and is usually 4 [32], so here it is set to 1, 4, and 100. To assess the impact of cyberattacks, the intensity from (1) is 30 and 100. The circular road considered is illustrated in Figure 3 and the simulation parameters are given in Table 1.  
Figure 4 presents the flow versus density with the proposed and ID models for \(S/S^{\prime}=0.2,\ 0.5\), and 0.8, and \(\delta=1,\ 4\), and 100, and the results are summarized in Tables 2 and 3, respectively. These show that with the proposed model, the maximum flow increases as \(S/S^{\prime}\) increases, whereas the critical density decreases. Similar behavior is observed with the ID model as \(\delta\) increases. However, the road capacity with the proposed model is higher. As the density increases, the distance headway decreases, and thus \(S/S^{\prime}\) is  
Figure 3: The simulation environment with a circular road. smaller. In dense traffic (\(S/S^{\prime}=0.2\)), the capacity with the proposed model is 1.4 times higher than the capacity with the ID model for \(\delta=100\). \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Desired speed for the ID model, \(V_{k}^{\prime}\) & 30 m/s [60] \\ Desired speed for the proposed model, \(V_{k}^{\prime}\) & 20 m/s [61] \\ Time headway for the proposed model, \(T_{k}\) & 1 s \\ Time headway for the ID model, \(T_{k}\) & 2 s \\ Maximum acceleration, \(a_{max}^{k}\) & 0.73 m/s\({}^{2}\)[32] \\ Jam spacing for the proposed model, \(j\) & 1.5 m \\ Maximum normalized density for the proposed model, \(\rho=1/j\) & 0.67 \\ Jam spacing for the ID model, \(j\) & 2 m \\ Maximum normalized density for the ID model, \(\rho=1/j\) & 0.5 \\ Deceleration, \(b_{min}^{k}\) & 1.67 m/s\({}^{2}\)[32] \\ Vehicle length, \(L\) & 4.5 m \\ CAV reaction time, \(R_{k}\) & 0.1 s \\ Ratio of distance headway to desired distance headway, \(S/S^{\prime}\) & 0.2, 0.5, and 0.8 \\ Time step size, \(\Delta t\) & 0.5 s [53] \\ Cyberattack intensity, \(c\) & 30 and 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 4: Fundamental diagram with the (**a**) proposed model and (**b**) ID model. Figure 5 presents the proposed model speed behavior on a 1 km circular road for \(S/S^{\prime}=0.2,\ 0.5\), and 0.8. This shows that as \(S/S^{\prime}\) increases, i.e., traffic approaches free flow and the speed becomes smooth over time, which is realistic. Conversely, with the ID model, traffic does not evolve towards a constant speed, and the variations increase over time and space with an increase in \(\delta\), as indicated in Figure 6. Figure 5a shows that with \(S/S^{\prime}=0.2\), the speed is between 17.9 m/s and 16.7 m/s from 1.0 s to 31.0 s, and there are small variations in speed. As \(S/S^{\prime}\) increases, these variations decrease, and at \(S/S^{\prime}=0.8\), the speed is approximately 17.9 m/s from 77.0 s to 200 s. With the ID model, for \(\delta=1\), the speed varies between 9.9 m/s and 10.2 m/s from \(-1000\) m to 0 m at 196.0 s as shown in Figure 6a. As \(\delta\) increases, the variations in speed increase, and with \(\delta=100\), the speed is between 9.6 m/s and 10.6 m/s with a difference of 1 m/s from \(-1000\) m to 0 m at 198.0 s as indicated in Figure 6c. This shows that the variations in speed are smaller with the proposed model.