# A Microscopic Traffic Model Considering Driver Reaction and Sensitivity
## 4 Simulation Results
The corresponding velocity with the proposed model for \(\frac{\tau}{\tau_{s}}<1\) (aggressive driver) is given in Figure 15. This indicates that the variations in velocity are smaller with a larger value of \(h\). The velocities with the proposed model for \(\frac{\tau}{\tau_{s}}>1\) (sluggish driver) and \(\frac{\tau}{\tau_{s}}=1\) (typical driver) are presented in Figures 16 and 17, respectively. These show that the variations in velocity increase with \(h\). Figure 12: Flow with the proposed model over a 1200 m circular road for \(\frac{\tau}{\tau_{s}}>1\) and \(h=0.3,\ 0.5,\) and \(1.0\). Figure 13: Flow with the proposed model over a 1200 m circular road for \(\frac{\tau}{\tau_{s}}=1\) and \(h=0.3,\ 0.5,\) and \(1.0\). Figure 18 presents the density evolution over time and distance with the ID model. When \(\delta=1\), the density is 0.012 from 0 to 136.5 m at 149.5 s. At 336.3 m, it is 0.03 and then decreases to 0.016 at 709.2 m as shown in Figure 18a. From 0 to 47.0 s, there is a traffic queue as the density is 0.20. At 80.5 s, the density at 148.0 s decreases to 0.032 after the congestion ends. When \(\delta=4\), at 147.0 s the density is 0.014 from 0 to 23.3 m. It increases to 0.036 at 219.8 m and then decreases to 0.014 at 619.4 m as shown in Figure 18b. From 0 to 45.0 s, the density is 0.20, which indicates a traffic queue. At 149.00 s, the density decreases to 0.036. When \(\delta=20\), at 147.0 s the density between \(-66.6\) m and \(-50.0\) m is 0.20, which indicates a traffic queue. At 509.9 m, it decreases to 0.008 as shown in Figure 18c. It is 0.20 from 0 to 46.5 s, so there is a traffic queue. The density then decreases to 0.05 at 66.0 s. A queue again develops at 77.0 s as the density is 0.20 and remains until 150.0 s between \(-66.6\) and \(-50.0\) m. Figure 18 shows that as \(\delta\) increases, the change in density over time increases, which indicates the model is unstable. Figure 14: Velocity with the ID model for \(\delta=1,\ 4\), and 20 over a 1200 m circular road. Figure 15: Velocity with the proposed model for \(h=0.3,\ 0.5\), and 1.0 with \(\frac{\tau}{\tau_{s}}<1\) over a 1200 m circular road. Figure 19 presents the density evolution over time and distance with the proposed model for \(\frac{\tau}{\tau_{\rm s}}<1\) (aggressive driver). With \(h=0.3\), from 0 to 53.3 m at 149.0 s the density is 0.01. It increases to 0.06 at 129.8 m and then decreases to 0.016 at 456.2 m as shown in Figure 19a. From 0 to 79.0 s, the density is 0.20, which indicates a traffic queue. At 114.5 s, the queue dissipates and the density decreases to 0.05 and then increases to 0.06 at 149.0 s. With \(h=0.5\), from 0 to 336.3 m at 148.5 s, the density is 0.012. It increases to 0.03 at 492.8 m and then decreases to 0.016 at 885.7 m as shown in Figure 19b. From 0 to 49.5 s, the density is 0.20, which indicates a queue, and at 149.0 s, it decreases to 0.035. With \(h=1.0\), from 0 to 732.6 m at 149.5 s the density is 0.014. At 985.6 m it increases to 0.020 as shown in Figure 19c. From 0 to 43.0 s, the density is 0.20, which indicates a queue. At 146.0 s, the queue dissipates and the density decreases to 0.015 at 169.8 m.  
Figure 16: Velocity with the proposed model for \(h=0.3,\ 0.5\), and 1.0 with \(\frac{\tau}{\tau_{\rm s}}>1\) over a 1200 m circular road. Figure 17: Velocity with the proposed model for \(h=0.3,\ 0.5\), and 1.0 with \(\frac{\tau}{\tau_{\rm s}}=1\) over a 1200 m circular road. Figure 20 presents the density evolution over time and distance with the proposed model for \(\frac{\tau}{t_{c}}>1\) (sluggish driver). With \(h=0.3\), from 0 to 26.6 m, the density is 0.014  
Figure 19: Traffic density with the proposed model over a 1200 m circular road for \(\frac{\tau}{t_{c}}<1\) and (**a**) \(h=0.3\), (**b**) \(h=0.5\), and (**c**) \(h=1.0\). Figure 10:0 Traffic density with the ID model over a 1200 m circular road for (**a**) \(\delta=1\), (**b**) \(\delta=4\), and (**c**) \(\delta=20\).