# A Microscopic Traffic Flow Model Characterization for Weather Conditions
## 5 Performance Evaluation
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Weather Severity** & **Maximum Flow** & **Maximum Density** & **Critical Velocity** \\
**Index \(\alpha\)** & **(veh/s)** & **Maximum Density** & **(m/s)** \\ \hline
0 & 0.433 & 0.017 & 24.5 \\
0.3 & 0.426 & 0.019 & 22.4 \\
0.55 & 0.413 & 0.021 & 19.3 \\
0.7 & 0.397 & 0.023 & 17.3 \\
0.8 & 0.376 & 0.025 & 15.0 \\
0.9 & 0.328 & 0.028 & 11.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum flow and density, and critical velocity for the proposed model. Figure 4: _Cont._  
For the proposed model with \(\alpha~{}=~{}0\), the queue exists between 0 s and 44.5 s. The velocity after the queue dissipates varies between 1.27 m/s and 1.80 m/s. The queue appears again at 86.5 s and lasts until 120 s, as shown in Figure 4d. With \(\alpha~{}=~{}0.3\), the queue exists between 0 s and 45.0 s, and the velocity after the queue dissipates varies between 1.42 m/s and 2.10 m/s. The queue again develops at 91.5 s and lasts until 120 s, as shown in Figure 4e. With \(\alpha~{}=~{}0.55\), the queue dissipates at 42.5 s, as shown in Figure 4f, and the corresponding velocity is 1.53 m/s. With \(\alpha~{}=~{}0.7\) and \(\alpha~{}=~{}0.8\), the queue dissipates at 43.0 s and 45.0 s, respectively, as shown in Figure 4g.h. The corresponding velocity is 1.60 m/s and 2.30 m/s, respectively. With \(\alpha~{}=~{}0.9\), the queue dissipates at 48.0 s, and the corresponding velocity is 2.50 m/s, as shown in Figure 4g. With \(\alpha~{}=~{}0,~{}0.3\) and \(\alpha~{}=~{}0.55\), the maximum velocity is 25.0 m/s, with \(\alpha~{}=~{}0.7\) and \(\alpha~{}=~{}0.8\) it is 20.0 m/s, and with \(\alpha~{}=~{}0.9\) it is 15.0 m/s. Figure 5 presents the time-space vehicle trajectories for a platoon of 15 vehicles with the ID and proposed models over a circular road of length 800 m. The red trajectory is for the first vehicle, and the black trajectories are for the remaining 14 vehicles that follow the 1 st vehicle. The positions with the ID and proposed models of the 1 st, 6 th, and 10 th vehicles at 40 s are given in Table 6. These results show that for the ID model with \(\delta~{}=~{}1\), the position of the 1 st and 6 th vehicles is \(429.4\) m and \(84.77\) m, respectively, and the position of the 10 th vehicle is \(-34.83\) m, as shown in Figure 5a. With \(\delta~{}=~{}4\), the position of the 1 st and 6 th vehicles is \(522.3\) m and \(116.1\) m, respectively, as shown in Figure 5b, while with \(\delta~{}=~{}20\), the position of the 1 st and 6 th vehicles is \(532.5\) m and \(116.5\) m, respectively, as shown in Figure 5c. With \(\delta~{}=~{}4\) and \(\delta~{}=~{}20\), the position of the 10 th vehicle is \(-28.58\) m and \(-28.57\) m, respectively. For the proposed model with \(\alpha~{}=~{}0\), the position of the 1 st and 6 th vehicles is \(532.4\) m and \(116.5\) m, respectively, as shown in Figure 5d. With \(\alpha~{}=~{}0.3\), the position of the 1 st and 6 th vehicles is \(531.7\) m and \(116.5\) m, respectively, as shown in Figure 5e, while with \(\alpha~{}=~{}0.55\), the position of the 1 st and 6 th vehicles is \(528.5\) m and \(116.5\) m, respectively, as shown in Figure 5f. With \(\alpha~{}=~{}0.3\) and \(0.55\), the position of the 10 th vehicle is \(-28.57\) m, as shown in Figure 5d-f. With \(\alpha~{}=~{}0.7\), the position of the 1 st and 6 th vehicles is \(520.6\) m and \(119.5\) m, respectively, while the position of the 10 th vehicle is \(-28.58\) m, as shown in Figure 5g. With \(\alpha~{}=~{}0.8\), the position of the 1 st and 6 th vehicles is \(505.0\) m and \(113.5\) m, respectively, while the position of the 10 th vehicle is \(-28.71\) m, as shown in Figure 5h. With \(\alpha~{}=~{}0.9\), the position of the 1 st and 6 th vehicles is \(453.3\) m and \(95.8\) m, respectively, while the position of the 10 th vehicle is \(-31.75\) m, as shown in Figure 5i. Table 6 indicates that as the exponent \(\delta\) increases, the distance covered by the 1 st and 6 th vehicles increases, whereas the distance covered by the 10 th vehicle decreases.