## 6 Simulation Results
Figure 17 shows the [PERSON] model's density compared with the proposed model's density behavior during 75 s. The [PERSON] model's density behavior was more oscillatory prior to the 50 th time step than in the proposed model. Figure 16: Density behavior of the proposed model over a 300 m circular road at different time steps during 75 s.  
Figure 15: The [PERSON] model’s velocity behavior on a 300 m circular road at 1 s at 5 s,15 s, 37.5 s, and 50 s.  
Figure 18 shows the proposed model velocity behavior over a 300 m circular road for 75 s. The velocity ranged from 3.6 m/s to 8.3 m/s. The variation in velocity shown in Figure 17 corresponds to the density behavior in Figure 16. The velocity was within the prescribed minimum of 0 m/s and a maximum of 9 m/s. Figure 19 compares the velocity behavior of the proposed and [PERSON]'s models. The velocity ranged from \(-\)1.5 m/s to 12.6 m/s, which was an oscillatory and unusual behavior. The traffic velocity over the distance cannot be negative with time. The velocity of [PERSON]'s model prior to the 50 th time step did not stay within the employed range. For example, at the 50 th distance step and 10 th time step, [PERSON]'s model gave a velocity of 8.1 m/s, while the proposed model gave a velocity of 8.3 m/s. This suggests that both models provided comparable velocity predictions, with the proposed model slightly exceeding the [PERSON] model's value. At the 200 th distance step and 10 th time step, [PERSON]'s model gave a velocity of 6.4 m/s, as shown in Figure 17, while the proposed model's velocity was 3.7 m/s, as shown in Figure 14.0 This indicates that both models provided similar velocity predictions but with the proposed model's velocity values being lower than those of [PERSON]'s model. However, at the 250 th distance step and 10 th time step, [PERSON]'s model gave a velocity of 9.1 m/s, exceeding the maximum expected velocity value of 9 m/s, as shown in Figure 14.1 Thus, in some cases, [PERSON]'s model provided higher velocity predictions than the expected maximum. The density and velocity for [PERSON]'s and the proposed models at the 10 th time step (5 s) for a 300 m road are summarized in Figure 14.2 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**[PERSON]’s Model**} & \multicolumn{2}{c}{**Proposed Model**} \\ \cline{3-6}
**S. No** & **Distance Step (Ax) and Time Step (\(\Delta\)t = 10)** & **Density** & **Velocity** & **Density** & **Velocity** (m/s)** \\ \hline
1 & \(\Delta\)x = 50 & 0.094 & 8.10 & 0.075 & 8.30 \\ \hline
2 & \(\Delta\)x = 100 & 0.190 & 0.19 & 0.099 & 8.10 \\ \hline
3 & \(\Delta\)x = 150 & 0.430 & 4.01 & 0.610 & 3.50 \\ \hline
4 & \(\Delta\)x = 200 & 0.390 & 6.40 & 0.500 & 3.70 \\ \hline
5 & \(\Delta\)x = 250 & 0.220 & 9.10 & 0.098 & 8.10 \\ \hline
6 & \(\Delta\)x = 300 & 0.078 & 6.70 & 0.099 & 8.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of [PERSON]’s and the proposed models’ density and velocity behavior for the 300 m road at the 10 th time step. Figure 17: The [PERSON] model’s density behavior over a 300 m circular road at different time steps during 75 s.  
With [PERSON]'s model, the changes in velocity were significant, while the proposed model showed minor changes in velocity, as shown in Table 7, suggesting that the [PERSON] model's velocity behavior was more oscillatory and unrealistic. Thus, [PERSON]'s model inadequately characterized traffic behavior. Furthermore, the proposed model took into account traffic emissions and could, therefore, make traffic emission predictions, while [PERSON]'s model could not. In the proposed model, as the velocity increased, the emissions decreased, as expected. For example, at the 100 th distance step and 10 th time step, the emission value, based on velocity in the proposed model, was 8.7 kg CO\({}_{2}\)/km. Based on the correct depiction of the corresponding density behavior shown in Figure 17, the proposed model's lower velocity resulted in more accurately calculated lower emissions.