# A Microscopic Traffic Flow Model Characterization for Weather Conditions
## 5 Performance Evaluation  
Both the ID and proposed models are evaluated over a circular road of length 800 m, with a platoon of 15 vehicles for 120 s, using MATLAB. It is commonly employed for performance evaluation, as it is an interactive environment that integrates numerical and symbolic computations with scientific visualization [43]. MATLAB has a simple language that is ideal for quick prototyping. It can be more expensive than conventional C or Python compilers [44], but this is more than offset by the reduced development time [44]. The explicit Euler scheme [41] with time step 0.5 s is employed to implement both models. The simulation parameters are given in Table 2. The maximum velocity is 33.3 m/s, the time headway is 2 s [42], and the minimum and maximum acceleration are 0.73 m/s\({}^{2}\) and 1.67 m/s\({}^{2}\), respectively [20]. The vehicle length is 5 m [41] and the distance headway is 25 m [40]. The proposed model is evaluated with \(\alpha~{}=~{}0,~{}0.3,~{}0.55,~{}0.7,~{}0.8\), and 0.9, and the ID model with \(\delta~{}=~{}1,4\), and 20. For a platoon of 15 vehicles, the jam spacing is 7 m [41] and the maximum normalized density is \(\frac{1}{s_{j}}~{}=~{}0.143\). For a platoon of 30 vehicles, the jam spacing is 2 m [20] and the maximum normalized density is \(\frac{1}{s_{j}}~{}=~{}0.5\). The traffic flow behavior of the ID and proposed models is given in Figure 2. This shows that for \(\delta~{}=~{}1\), the maximum flow with the ID model is 0.310 veh/s at a density of 0.028. The corresponding velocity is 11.1 m/s, as shown in Figure 3. With \(\delta~{}=~{}4\), the maximum flow is 0.400 veh/s at a density of 0.024, and the corresponding velocity is 16.30 m/s. With \(\delta~{}=~{}20\), the maximum flow is 0.440 veh/s at a density of 0.016, and the corresponding velocity is 27.5 m/s, as shown in Figure 3. Table 3 indicates that the maximum flow and velocity increase with \(\delta\), whereas the density decreases. \begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value** \\ \hline Maximum velocity, \(v_{max}\) & 33.3 m/s \\ Maximum normalized density for 15 vehicle & \(\frac{1}{s_{j}}~{}=~{}0.143\) \\ platoon, \(\rho_{m}\) at \(v~{}=~{}0\) m/s & 1 \\ Maximum severity index, \(\alpha_{m}\) & 25 m \\ Distance headway, \(H\) & 2\(\mathrm{s}\) \\ Time headway, \(T\) & 2 s \\ Weather severity index, \(\alpha\) & 0, 0.3, 0.55, 0.7, 0.8, and 0.9 \\ Jam spacing for 15 vehicle platoon, \(s_{j}\) & 7m \\ Minimum acceleration, \(a\) & 0.73 m/s\({}^{2}\) \\ Maximum acceleration, \(b\) & 1.67 m/s\({}^{2}\) \\ Vehicle length, \(L\) & 5m \\ Time step, \(\Delta t\) & 0.5 s \\ Jam spacing for 30 vehicle platoon, \(s_{j}\) & 2 m \\ Maximum normalized density for 30 vehicle & \(\frac{1}{s_{j}}~{}=~{}0.5\) \\ platoon, \(\rho_{m}\) at \(v~{}=~{}0\) m/s & \(\frac{1}{s_{j}}~{}=~{}0.5\) \\ \hline \end{tabular}
\end{table} 
Table 2: Simulation Parameters. decreases as \(\alpha\) increases, whereas the maximum density increases and the corresponding velocity decreases. Figure 4 presents the time-space velocity evolution of the queue due to traffic congestion for the ID and proposed models. This shows that, initially, the velocity in the queue is zero. For the ID model with \(\delta~{}=~{}1\), the queue dissipates at 45.5 s, as shown in Figure 4a, while with \(\delta~{}=~{}4\), the queue dissipates at 44.0 s, as shown in Figure 4b. The corresponding velocity is 1.26 m/s and 1.14 m/s, respectively. With \(\delta~{}=~{}20\), the initial queue dissipates at 43.5 s, and the velocity after the queue is 1.01 m/s, as shown in Table 5. The queue again develops at 78.0 s and lasts until 120 s, as shown in Figure 4c. With \(\delta~{}=~{}1\), the maximum velocity is 15.0 m/s, while with \(\delta~{}=~{}4\) and \(\delta~{}=~{}20\), the maximum velocity is 20.0 m/s and 25.0 m/s, respectively. These results show that the maximum velocity increases as \(\delta\) increases.