# A New Driver Model Based on Driver Response
## 5 Performance Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Time Headway \(T\) (s)**} & **Maximum Flow (veh/s)** & \multirow{2}{*}{**Maximum Density**} & **Critical Velocity (m/s)** \\ \hline
0.1 & 0.49 & 0.028 & 17.6 \\
0.3 & 0.60 & 0.038 & 15.7 \\
0.5 & 0.59 & 0.041 & 14.4 \\
1 & 0.51 & 0.038 & 13.4 \\
1.6 & 0.41 & 0.031 & 13.4 \\
1.7 & 0.40 & 0.030 & 13.6 \\
2 & 0.36 & 0.025 & 14.0 \\
2.7 & 0.30 & 0.021 & 14.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum flow, maximum density, and critical velocity for the proposed model. Figure 4: Velocity behaviour of the ID and proposed models over a circular road of length 800 m.  
Figure 5: _Cont_. For the proposed model with \(T=0.1\) s, the traffic queue did not dissipate. At 0 s, the velocity between \(-96.5\) m and \(-3.3\) m was 0 m/s. At 60 s, the velocity was 0 m/s between \(-49.0\) m and \(-96.5\) m, while at 120 s the velocity was 0 m/s from \(-89.0\) m to \(-96.5\) m, as shown in Figure 5d. With \(T=0.5\) s and 1 s, the queue dissipated at 45.0 s and 39.5 s, respectively, as shown in Figure 5e.f. With \(T=0.5\) s, the velocity after the queue was 1 m/s, while with \(T=1\) s, this velocity was 0.9 m/s, as indicated in Table 5. With \(T=1.6\) s and 2.7 s, the queue dissipated at 41.0 s and 45.5 s, respectively, as shown in Figure 5g.h. At \(T=1.6\) s, the velocity increased from 0 m/s to 0.8 m/s after 41.0 s as given in Table 5. At \(T=2.7\) s, the velocity increased from 0 m/s to 0.6 m/s after 45.5 s. The maximum velocity attained with the proposed model at \(T=0.1\) s was 10 m/s, while with \(T=0.5,\ 1,\ 1.6\), and 2.7 s it was 20 m/s, as shown in Figure 5d-h. Note that with \(T=0.1\) s, the traffic queue did not dissipate. The largest velocity with the proposed model after the queue was 1 m/s, which was observed with \(T=0.5\) s. The results for non-uniform traffic conditions are given in Figure 5i. This shows that the queue dissipated at 40.5 s. The velocity after 40.5 s was 0.7 m/s, increased to 8.7 m/s at 74.0 s, and then decreased to 2.4 m/s at 119.5 s.  
The time-space vehicle trajectories for the ID and proposed models are given in Figure 6 and the results are summarized in Table 6. This shows the velocity changes for a platoon of 15 vehicles with an initial average velocity of 15 m/s over an 800 m circular road. The red trajectory corresponds to the first vehicle that starts moving at \(t=0\) s, while the black trajectories are the following 14 vehicles. With \(\delta=1\) and 4, the queue existed for 45.0 s and 43.5 s, respectively, as shown in Figure 6a,b. Further, the 15 th vehicle was in the queue for 45.0 s at \(-91.8\) m and 43.5 s at \(-93.1\) m, respectively, as shown in Figure 6a,b. With \(\delta=20\), the queue existed for 43.5 s. The first vehicle was in the queue for 2.0 s at 1.2 m, while the 15 th vehicle was in the queue for 43.5 s at \(-93.1\) m. A queue again appeared at 86.0 s at 50.0 m and increased up to 120 s with the queue between 59.4 m and 94.7 m, as shown in Figure 6c. Figure 5: Velocity over time and space for 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. Velocity over time and space for the ID and proposed models over a circular road of length 800 m: **(g)** proposed model, \(T=1.6\) s; **(h)** proposed model, \(T=2.7\) s; **(i)** proposed model, rearward velocity 33.3 m/s, forward velocity 24.5 m/s, rearward time headway 4 s, and forward time headway 5 s.