# Evaluating the Effect of Road Surface Potholes Using a Microscopic Traffic Model
## 3 Performance Evaluation
### Performance Results  
Figure 6 presents the velocity evolution over time for the ID model on a 1 km circular road. The red line gives the velocity of the first vehicle and the black lines correspond to the velocity of the following vehicles. With \(\delta=1.0\), the variations are small and decrease over time. The velocity is between 13.6 and 21.6 m/s at 200 s as shown in Figure 6a. With \(\delta=4.0\) and 200, the variations in velocity are larger and increase over time as shown in Figure 6b,c. With \(\delta=4.0\), the velocity is between 0.26 and 28.6 m/s at 200 s, and with \(\delta=200\) it is between 0.21 and 33.1 m/s at 200 s. Thus, an increase in \(\delta\) results in an increase in the variations in velocity. Figures 7-9 present the velocity evolution over time for the proposed model with small, medium, and large potholes, respectively. The red lines indicate the velocity of the first vehicle and the black lines correspond to the velocity of the following vehicles. For small potholes, with an aggressive driver, the variations over time are large and the velocity is between 0.74 and 13.2 m/s at 200 s, as shown in Figure 7a. With a sluggish driver, the variations are small and decrease over time. The velocity is between 18.6 and 25.6 m/s at 200 s, as shown in Figure 7b. With a typical driver, as expected the behavior is between that of aggressive and sluggish drivers with a velocity between 15.1 and 22.9 m/s at 200 s, as shown in Figure 7c. For medium potholes, with an aggressive driver the variations in velocity over time are small and between 14.9 and 22.6 m/s at 200 s, as shown in Figure 8a. With sluggish and typical drivers, the variations are large and increase over time, as shown in Figure 8b,c. With a sluggish driver, at 200 s the velocity is between 0.20 and 31.9 m/s, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pothole** & **Driver** & **Maximum Flow** & **Critical Density** & **Critical Velocity** \\
**Size** & **Sensitivity** & **(veh/s)** & **Critical Density** & **(m/s)** \\ \hline \multirow{3}{*}{Small} & Aggressive & 0.41 & 0.068 & 6.2 \\  & Sluggish & 0.82 & 0.064 & 12.8 \\  & Typical & 0.73 & 0.075 & 9.8 \\ \hline \multirow{3}{*}{Medium} & Aggressive & 0.73 & 0.066 & 9.8 \\  & Sluggish & 0.91 & 0.036 & 24.9 \\  & Typical & 0.89 & 0.043 & 20.8 \\ \hline \multirow{3}{*}{Large} & Aggressive & 0.86 & 0.055 & 15.5 \\  & Sluggish & 0.93 & 0.031 & 28.9 \\ \cline{1-1}  & Typical & 0.92 & 0.034 & 26.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum flow, critical density, and velocity for the proposed model with small, medium, and large potholes. Figure 5: Fundamental diagrams for the proposed model with large potholes (**a**) flow–density and (**b**) velocity–density. and with a typical driver, it is between 0.28 and 30.4 m/s. For large potholes, the variations in velocity over time are large for all three types of drivers, as shown in Figure 9. With an aggressive driver, the velocity is between 0.38 and 28.5 m/s at 200 s, as shown in Figure 9a. The corresponding velocity for a sluggish driver is between 0.26 and 32.9 m/s and for a typical driver is between 0.16 and 32.4 m/s as shown in Figure 9b,c, respectively. Figure 6: Velocity with the ID model on a 1 km circular road for (**a**) \(\delta=1.0\) ; (**b**) \(\delta=4.0\) ; and (**c**) \(\delta=200\). Figure 7: Velocity for the proposed model on a 1 km circular road with small potholes and an (a) aggressive driver; (**b**) sluggish driver; and (**c**) typical driver. Figure 8: Velocity for the proposed model on a 1 km circular road with medium potholes and an (a) aggressive driver; (b) sluggish driver; and (c) typical driver. Figure 9: Velocity for the proposed model on a 1 km circular road with large potholes and an (**a**) aggressive driver; (**b**) sluggish driver; and (**c**) typical driver. Figure 10 presents the acceleration over time of a single vehicle for the ID model on a 1 km circular road. For all values of \(\delta\), the acceleration is initially 0.73 m/s\({}^{2}\) and then varies over time.