# Evaluating the Effect of Road Surface Potholes Using a Microscopic Traffic Model
## 3 Performance Evaluation
### Performance Results
Figures 15-17 present the time and space flow behavior for the proposed model with small, medium, and large size potholes, respectively, on a 1 km circular road. For small potholes, with an aggressive driver, the flow is 0 at 1.0 s and increases to 0.55 veh/s at 105.5 s. It increases to 0.67 veh/s at 198.0 s and 116.5 m. At 26.6 m, the flow is 0.31 veh/s at 200 s. It increases to 0.67 veh/s and then decreases to 0.31 veh/s at 879.1 m, as shown in Figure 15a. Figure 15b indicates that with a sluggish driver, the flow is 0 at 1.0 s and increases to approximately 0.82 veh/s between 65.5 and 195.0 s. It is 0.76 veh/s at 198.0 s and 869.1 m. At \(-\)106.5 m, the flow is 0.77 veh/s at 200 s, decreases to 0.63 veh/s at 569.4 m, and then increases to 0.76 veh/s at 869.1 m. Figure 15c shows that with a typical driver, the flow is 0 at 1.00 s and increases to approximately 0.73 veh/s between 74.5 and 195.0 s. It is 0.73 veh/s at 200 s and 869.1 m. At \(-\)103.2 m, the flow is 0.69 veh/s at 199.0 s, decreases to 0.52 veh/s between 569.0 and 719.2 m, and then increases to 0.73 veh/s at 869.1 m. Figure 15 indicates that the flow with a typical driver is smoother than with sluggish and aggressive drivers. For medium potholes, with an aggressive driver, the flow is initially 0 and increases to approximately 0.72 veh/s between 75.0 and 195.0 s. It is 0.70 veh/s at 198.0 s and 862.4 m as shown in Figure 16a. At \(-\)123.2 m, the flow is 0.69 veh/s at 198.0 s, approximately 0.53 veh/s between 489.5 and 699.3 m, and 0.70 veh/s at 862.4 m. With a sluggish driver, the initial flow is 0, increases to 10.80 veh/s at 82.5 s, and then varies between 0.90 and 13.05 veh/s, as shown in Figure 16b. Similarly, the initial flow with a typical driver is 0, increases to 11.80 veh/s at 94.5 s, and then varies between 0.40 and 12.30 veh/s as shown in Figure 16c. With sluggish and typical drivers, the flow over space first increases to 13.9 veh/s at 192.5 s and 12.3 veh/s at 193.5 s, respectively, and then decreases to 0.30 veh/s at 198.0 s. Figure 16 indicates that with an aggressive driver, the flow is smoother than with sluggish and typical drivers, but the maximum flow is small. For large potholes, with an aggressive driver, the flow is initially 0, increases to 6.60 veh/s at 86.5 s, and then varies between 0.70 and 12.10 veh/s, as shown in Figure 17a. With a  
Figure 5:1 Single vehicle acceleration for the proposed model on a 1 km circular road with large potholes. sluggish driver, Figure 17b shows that the initial flow is 0, increases to 7.19 veh/s at 68.5 s, and then varies between 0.70 and 13.80 veh/s. Similarly, with a typical driver the initial flow is 0, increases to 5.80 veh/s at 64.0 s, and then varies between 1.40 and 13.60 veh/s, as shown in Figure 17c. With aggressive, sluggish, and typical drivers the flow over space first increases to 12.10 veh/s at 198.0 s, 13.80 veh/s at 197.5 s, and 13.60 veh/s at 197.0 s, respectively, then decreases to 0.30 veh/s at 200 s.  
Figure 5:2 Time–space flow behavior over a 1 km road for the ID model with (**a**) \(\delta=1.0\) ; (**b**) \(\delta=4.0\); and (**c**) \(\delta=200\). Figure 5:3 Time–space flow behavior for the proposed model with small potholes and an (**a**) aggressive driver; (**b**) sluggish driver; and (**c**) typical driver. Figure 5:4 Time–space flow behavior for the proposed model with medium potholes and an (**a**) aggressive driver; (**b**) sluggish driver; and (**c**) typical driver. The results presented in this section illustrate that the proposed model effectively characterizes the velocity and acceleration based on road surface conditions. An increase in pothole size increases the variations in velocity. With sluggish and typical drivers, the variations in velocity are smaller with small potholes compared to an aggressive driver, whereas with medium and large potholes these variations are large. Furthermore, with all three driver types the variations in acceleration increase with pothole size.