# A Microscopic Traffic Model Considering Driver Reaction and Sensitivity
## 4 Simulation Results  
The performance of the proposed and ID models is evaluated over a single-lane circular road of length 1200 m for 150 s using the explicit Euler method [5] with a time step of 0.5 s. There are no vehicle exits or entrances on the road. The ID model is evaluated with time headway 2 s. The proposed model is evaluated with \(\tau=1\) s (sensitivity \(\frac{\tau}{\tau_{s}}<1\)), which corresponds to an aggressive driver, \(\tau=2.5\) s (sensitivity \(\frac{\tau}{\tau_{s}}>1\)), which corresponds to a sluggish driver, and \(\tau=2\) s (sensitivity \(\frac{\tau}{\tau_{s}}=1\)), which corresponds to a typical driver. The value of \(h=\frac{\delta}{\beta}\) ranges between 0 and 1, so here 0.3, 0.5, and 1.0 are used. The value of the acceleration exponent \(\delta\) varies between 1 and \(\infty\), and is usually 4 [17], so \(\delta=1,4\), and 20 are employed. The maximum normalized density is \(\frac{1}{\delta_{j}}=0.2\) and a platoon of 21 vehicles is considered. The simulation parameters are given in Table 3.  
Figure 4 presents the flow and velocity with the ID model and the results are summarized in Table 4. When \(\delta=1\), the maximum flow is 0.33 veh/s at a density of 0.03, and the corresponding velocity is 9.9 m/s. When \(\delta=4\), the maximum flow is 0.42 veh/s at a density of 0.02, and the corresponding velocity is 16.9 m/s  
Figure 5 presents the flow and velocity with the proposed model for \(h=0.3,~{}0.5\), and \(1.0\), and the results are summarized in Table 5. With \(\frac{\tau}{\tau_{a}}>1\) (aggressive driver), the maximum flow at \(h=0.3\) is \(0.32\) veh/s at a density of \(0.03\), and the corresponding velocity is \(9.4\) m/s. For \(h=0.5\), the maximum flow is \(0.40\) veh/s at a density of \(0.04\), and the corresponding velocity is \(10.2\) m/s. For \(h=1.0\), the maximum flow is \(0.52\) veh/s at a density of \(0.05\), and the corresponding velocity is \(11.3\) m/s. With \(\frac{\tau}{\tau_{a}}>1\) (sluggish driver), the maximum flow at \(h=0.3\) is \(0.30\) veh/s at a density of \(0.03\), and the corresponding velocity is \(10.3\) m/s. For \(h=0.5\), the maximum flow is \(0.33\) veh/s at a density of \(0.02\), and the corresponding velocity is \(13.2\) m/s. For \(h=1.0\), the maximum flow is \(0.35\) veh/s at a density of \(0.02\), and the corresponding velocity is \(17.2\) m/s. With \(\frac{\tau}{\tau_{a}}=1\) (typical driver), at \(h=0.3\), the maximum flow is \(0.33\) veh/s at a density of \(0.04\), and the corresponding velocity is \(9.2\) m/s. For \(h=0.5\), the maximum flow is \(0.37\) veh/s at a density of \(0.03\), and the corresponding velocity is \(11.3\) m/s. For \(h=1.0\), the maximum flow is \(0.41\) veh/s at a density of \(0.03\), and a density of \(0.03\), and the corresponding velocity is \(12.1\) m/s. Table 5 indicates that with an aggressive driver, an increase in \(h\) increases the maximum flow, density, and velocity. However, with sluggish and typical drivers, an increase in \(h\) increases the maximum flow and velocity but decreases the density. Moreover, with an aggressive driver, an increase in \(h\) results in a faster increase in the maximum flow compared to a sluggish driver. As expected, with a typical driver the flow and velocity behavior are between the results for aggressive and sluggish drivers. Figure 6 presents the temporal and spatial evolution of a queue for the ID model, and the congestion results are summarized in Table 6. This shows that the velocity within the queue is zero. When \(\delta=1\), the queue dissipates at 57.5 s as shown in Figure 6a, and the corresponding velocity is 1.3 m/s. When \(\delta=4\), the queue dissipates at 56.0 s as shown in Figure 6b, and the corresponding velocity is 1.2 m/s. When \(\delta=20\), the queue exists from 0 to 55.5 s, and the velocity after the queue dissipates varies between 1.1 and 5.2 m/s. However, a new queue forms at 84.5 s and remains until 150.0 s, spanning 40.0 to 53.3 m as shown in Figure 6c.