# A Microscopic Traffic Model Considering Driver Reaction and Sensitivity
## 4 Simulation Results
With \(\delta=2\), the 1 st vehicle is at 958.9 m, while the 10 th vehicle is at 167.6 m and the 20 th vehicle is at \(-\)88.6 m. Table 8 indicates that as \(\delta\) increases, the distance traveled by the 1 st and 10 th vehicles increases but decreases for the 20 th vehicle. The temporal and spatial trajectories of the vehicles with the proposed model are presented in Figure 9 and the corresponding congestion results are given in Table 9. The positions of the 1 st, 10 th, and 20 th vehicles at 55.0 s are compared. For an aggressive driver, with \(h=0.3\), the 1 st vehicle is at 403.4 m, while the 10 th and 20 th vehicles are at \(-\)11.5 and \(-\)95.0 m, respectively. With \(h=0.5\), the first vehicle is at 519.3 m, while the 10 th and 20 th vehicles are at 60.6 and \(-\)94.9 m, respectively. With \(h=1.0\), the first vehicle is at 683.6 m,  
Figure 8: Trajectories of 21 vehicles with the ID model over a 1200 m circular road for (**a**) \(\delta=1\), (**b**) \(\delta=4\), and (**c**) \(\delta=20\). while the 10 th and 20 th vehicles are at 167.6 and \(-\)77.5 m, respectively. For a sluggish driver, with \(h=0.3\), the 1 st vehicle is at 801.5 m, while the 10 th and 20 th vehicles are at 95.9 and \(-\)92.8 m, respectively. With \(h=0.5\), the first vehicle is at 871.1 m, while the 10 th and 20 th vehicles are at 112.8 and \(-\)92.7 m, respectively. With \(h=1.0\), the first vehicle is at 923.8 m, while the 10 th and 20 th vehicles are at 117.9 and \(-\)92.7 m, respectively. For a typical driver, with \(h=0.3\), the 1 st vehicle is at 720.3 m, while the 10 th and 20 th vehicles are at 102.6 and \(-\)90.6 m, respectively. With \(h=0.5\), the first vehicle is at 815.3 m, while the 10 th and 20 th vehicles are at 141.3 and \(-\)88.8 m, respectively. With \(h=1.0\), the first vehicle is at 898.5 m, while the 10 th and 20 th vehicles are at 163.9 and \(-\)88.6 m, respectively. Table 9 indicates that for all three driver types, an increase in \(h\) increases the position (distance covered) of the 1 st and 10 th vehicles, whereas the position of the 20 th vehicle decreases. Figure 10 presents the traffic flow with the ID model over a 1200 m circular road for \(\delta=1,~{}4\), and 20. This shows that as \(\delta\) increases, the variations in the flow also increase. The corresponding flow with the proposed model for \(\frac{\tau}{\tau_{\rm s}}<1\) (aggressive driver) is given in Figure 11. This shows that a larger value of \(h\) results in smaller variations in flow. Figures 12 and 13 present the flow with the proposed model for \(\frac{\tau}{\tau_{\rm s}}>1\) (sluggish driver) and \(\frac{\tau}{\tau_{\rm s}}=1\) (typical driver), respectively. These show that the flow is larger with an increase in \(h\). Figure 11: Flow with the proposed model over a 1200 m circular road for \(\frac{\tau}{u_{i}}<1\) and \(h=0.3\), 0.5, and 1.0. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Driver** & \(h=\frac{s}{D}\) & **1 st Vehicle** & **10 th Vehicle** & **20 th Vehicle** \\
**Sensitivity** & **(m)** & **Position** & **Position** & **Position** \\ \hline \(\frac{\tau}{\tau_{i}}<1\) & 0.3 & 403.4 & \(-11.5\) & \(-95.0\) \\ (aggressive driver) & 0.5 & 519.3 & 60.6 & \(-94.9\) \\ (aggressive driver) & 1.0 & 683.6 & 167.6 & \(-77.5\) \\ \hline \(\frac{\tau}{\tau_{i}}>1\) & 0.3 & 801.5 & 95.9 & \(-92.8\) \\ (sluggish driver) & 0.5 & 871.1 & 112.8 & \(-92.7\) \\ \hline \(\frac{\tau}{\tau_{i}}=1\) & 0.3 & 720.3 & 102.6 & \(-90.6\) \\ (typical driver) & 0.5 & 815.3 & 141.3 & \(-88.8\) \\ 1.0 & 898.5 & 163.9 & \(-88.6\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Position of the 1 st, 10 th, and 20 th vehicles at 55.0 s with the proposed model. Figure 10: Flow with the ID model for \(\delta=1,~{}4\), and 20 over a 1200 m circular road. Figure 14 presents the velocity with the ID model over a 1200 m road for \(\delta=1,\ 4\), and 20. This shows that an increase in \(\delta\) increases the variations in velocity.