# A New Driver Model Based on Driver Response
## 5 Performance Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **Velocity during** & **Time** & **Velocity after Queue** & **Time** \\  & **Queue (m/s)** & **(s)** & **(m/s)** & **(s)** \\ \hline \(\delta=1\) & 0 & 0–45.0 & 1.7 & 45.0 \\ \(\delta=4\) & 0 & 0–43.5 & 1.6 & 43.5 \\ \(\delta=20\) & 0 & 0–43.5 and 86.0–120 & 1.4–6.4 & 43.5–86.0 \\ \(T=0.1\) s & 0 & 0–120 & Queue does not & - \\  & & & dissipate & \\ \(T=0.5\) s & 0 & 0–45.0 & 1 & 45.0 \\ \(T=1\) s & 0 & 0–39.5 & 0.9 & 39.5 \\ \(T=1.6\) s & 0 & 0–41.0 & 0.8 & 41.0 \\ \(T=2.7\) s & 0 & 0–45.5 & 0.6 & 45.5 \\ Non-uniform & 0 & 0–40.5 & 0.7 & 40.5 \\ traffic & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Velocity and time for the ID and proposed models during and after the queue. Figure 6: Trajectories of 15 vehicles with the ID and proposed models over a circular road of length 800 m: (**a**) ID model, \(\delta=1\); (**b**) ID model, \(\delta=4\); (**c**) ID model, \(\delta=20\); (**d**) proposed model, \(T=0.1\) s; (**e**) proposed model, \(T=0.5\) s; (**f**) proposed model, \(T=1\) s; (**g**) proposed model, \(T=1.6\) s; (**h**) proposed model, \(T=2.7\) s.  
For the proposed model with \(T=0.1\) s, the queue existed for 120 s and gradually dissipated. The first vehicle was in the queue for 3.0 s at 1.6 m, while the 15 th vehicle was in the queue for 120 s at \(-\)97.3 m, as shown in Figure 6d. With \(T=0.5\) s and 1 s, the queue existed for 45.0 s and 39.5 s, respectively, as shown in Figure 6e. Thus, the 15 th vehicle stayed for 45.0 s at \(-\)95.9 m and 39.5 s at \(-\)96.0 m, respectively. With \(T=1.6\) s and 2.7 s, the queue existed for 41.0 s and 45.5 s, respectively, as shown in Figure 6g.h. The 15 th vehicle was in the queue for 41.0 s at \(-\)96.05 m and 45.5 s at \(-\)96.06 m, respectively. The positions of the 1 st, 4 th and 10 th vehicles at 30 s with the ID and proposed models are now examined. With the ID model and \(\delta=1\), the position of the 1 st and 4 th vehicles was 261.9 m and 80.8 m, respectively, whereas the position of the 10 th vehicle was \(-\)58.9 m as shown in Figure 6a. With \(\delta=4\), the position of the 1 st and 4 th vehicles was 314.5 m and 101.1 m, respectively, as shown in Figure 6b. With \(\delta=20\), the position of the 1 st and 4 th vehicles was 317.7 m and 101.3 m, respectively, as shown in Figure 6c. The position of the 10 th vehicle with \(\delta=4\) and \(\delta=20\) was \(-\)58.3 m, as shown in Figure 6b.c. With the proposed model and \(T=0.1\) s, the position of the 1 st and 4 th vehicles was 88.7 m and \(-\)17.5 m at 30 s, respectively, and the position of the 10 th vehicle was \(-\)63.0 m, as shown in Figure 6d. With \(T=0.5\) s, the position of the 1 st and 4 th vehicles was 207.4 m and 64.7 m, respectively, and the position of the 10 th vehicle was \(-\)60.9 m at 30 s, as shown in Figure 6e. With \(T=1\) s, the position of the 1 st and 4 th vehicles was 262.2 m and 93.2 m at 30 s, respectively, and the position of the 10 th vehicle was \(-\)42.2 m as shown in Figure 6f. With \(T=1.6\) s, the position of the 1 st and 4 th vehicles was 289.7 m and 94.1 m, respectively, as shown in Figure 6g. With \(T=2.7\) s, the position of the 1 st and 4 th vehicles was 307 m and 75.8 m at 30 s, respectively, as shown in Figure 6h. The position of the 10 th vehicle with \(T=1.6\) and \(T=2.7\) was \(-\)58.3 m and \(-\)61.2 m, respectively. Table 6 indicates that as the acceleration exponent increased, the distance travelled by the 1 st and 4 th vehicles increased. However, the distance travelled by the 10 th vehicle decreased. Further, a decrease in the time headway decreased the distance travelled by the vehicles. Figure 7 presents the spatial and temporal traffic density behaviour with the ID and proposed models. This shows that with \(\delta=1\) for the ID model, the density between 0 m and 163.9 m at 119.5 s was 0.014. It increased to 0.02 at 369.6 m and then decreased to 0.016 at 602.7 m, as shown in Figure 7a.