# A New Driver Model Based on Driver Response
## 5 Performance Results  
The performance of the ID and proposed models was evaluated on a circular road of length 800 m for 120 s using the Euler technique with time step 0.5 s [16]. This technique was employed as it has been implemented in SUMO and AIMSUN for traffic prediction [16]. On a circular road, vehicle congestion can occur temporally, and large traffic changes can be expected. This is one of the worst conditions to evaluate traffic models. The simulation parameters are given in Table 2. The maximum velocity was 33.3 m/s, the average velocity was 15 m/s, and the jam spacing was 7 m [16]. The maximum normalized density was \(\frac{1}{s_{j}}=0.143\). The ratio of current density to the road capacity is called the normalized density. The ID model was evaluated with a time headway of 1.6 s [15], while the proposed model was evaluated with time headway values of 0.1, 0.5, 1, 1.6, and 2.7 s for uniform driver behaviour. Non-uniform driver behaviour was also examined with rearward velocity 33.3 m/s, rearward time headway 4 s, forward velocity 24.5 m/s, and forward time headway 5 s. The maximum acceleration and deceleration were 0.73 m/s\({}^{2}\) and 1.67 m/s\({}^{2}\), respectively [15]. The vehicle length was set to 5 m [16] as this typically varies between 2.7 and 5.6 m [44]. The values for \(h_{s}\) and \(h_{N}\) were 21 m and 25 m, respectively [45]. The acceleration exponent for the ID model ranges from 1 to \(\infty\) and is typically 4 [15], so \(\delta=1\), 4, and 20 were considered here. A string of 15 vehicles was investigated. As with most studies of vehicle behaviour, roadside data to compare with the numerical results is unavailable. For the proposed model, the maximum flow with \(T=0.1\) s and \(T=0.3\) s was 0.49 and 0.60 veh/s, respectively, at density 0.028 and 0.038. The corresponding velocities were 17.6 and 15.7 m/s, respectively. With \(T=0.5\) s and \(T=1\) s, the maximum flow was 0.59 and 0.51 veh/s, respectively, at density 0.041 and 0.038. The corresponding velocities were 14.4 and 13.4 m/s, respectively. With \(T=1.6\) s and \(T=1.7\) s, the maximum flow was 0.41 and 0.40 veh/s, respectively, at density 0.031 and 0.030. The corresponding velocities were 13.4 and 13.6 m/s, respectively. With \(T=2\) s and \(T=2.7\) s, the maximum flow was 0.36 and 0.30 veh/s, respectively, at density 0.025 and 0.021. The corresponding velocities were 14 and 14.1 m/s, respectively. Table 4 indicates that for the proposed model, the flow was a maximum at \(T=0.3\) s. Between \(T=0.1\) and 0.5 s, the density increased with \(T\), and above \(T=0.5\) s it decreased. For \(T\) between 0.1 and 1.7 s, the velocity decreased with \(T\) and above this value it increased. The spatial and temporal evolution of the queue caused by traffic congestion for the ID and proposed models is shown in Figure 5 and the results are tabulated in Table 5. The traffic velocity during the queue was zero, which is shown in yellow, and blue denotes the maximum velocity attained. For the ID model with \(\delta=1\), the queue dissipated at 45 s as shown in Figure 5a, while with \(\delta=4\) it dissipated at 43.5 s, as shown in Figure 5b. Table 5 indicates that with \(\delta=1\), the velocity after the queue was 1.7 m/s, while with \(\delta=4\), it was 1.6 m/s. With \(\delta=20\), the queue exists from 0 to 43.5 s and the corresponding velocity was 0 m/s. The velocity after the queue (after 43.5 s), varied between 1.4 m/s and 6.4 m/s as indicated in Table 5. A traffic queue again developed from 86 s to 120 s between 0 and 10 m, as shown in Figure 5c. Moreover, with \(\delta=1\), the maximum velocity was 20 m/s, while with \(\delta=4\) it was 25 m/s and with \(\delta=20\) it was 30 m/s, as shown in Figure 5a-c. These results indicate that the maximum velocity increased with \(\delta\).