# Evaluating the Effect of Road Surface Potholes Using a Microscopic Traffic Model
## 3 Performance Evaluation
### Performance Results
With \(\delta=1.0\), the acceleration is \(-0.59\) m/s\({}^{2}\) at 67.0 s and 0.22 m/s\({}^{2}\) at 88.5 s. At 162.00 s, it decreases to \(-0.72\) m/s\({}^{2}\) and then increases to 0.17 m/s\({}^{2}\) at 200 s. With \(\delta=4.0\), the acceleration is \(-1.31\) m/s\({}^{2}\) at 56.5 s and then varies between \(-1.67\) and 0.62 m/s\({}^{2}\). With \(\delta=200\), the acceleration is similar as it is \(-1.59\) m/s\({}^{2}\) at 53.5 s and then varies between 0.68 and \(-1.67\) m/s\({}^{2}\). Figure 10 indicates that larger variations in acceleration occur with a larger \(\delta\). Figures 11-13 present the acceleration over time of a single vehicle for the proposed model with small, medium, and large potholes, respectively. The initial acceleration is 0.73 m/s\({}^{2}\) and then varies over time. For small potholes, with an aggressive driver, the acceleration is \(-0.79\) m/s\({}^{2}\) at 98.5 s and increases to 0.05 m/s\({}^{2}\) at 200 s. With a sluggish driver, the acceleration is \(-1.08\) m/s\({}^{2}\) at 58.5 s and then is between 0.51 and \(-1.08\) m/s\({}^{2}\). With a typical driver, the acceleration is between \(-0.68\) and \(0.29\) m/s\({}^{2}\) which is between that of aggressive and sluggish drivers. Figure 11 shows that for small potholes the variations in acceleration are large with a sluggish driver. For medium potholes, Figure 12 shows that with an aggressive driver, the acceleration decreases to \(-0.67\) m/s\({}^{2}\) at 64.0 s and then increases to 0.28 m/s\({}^{2}\) at 84.5 s. It is \(-0.69\) m/s\({}^{2}\) at 153.0 s and 0.14 m/s\({}^{2}\) at 200 s. With a sluggish driver, the acceleration varies between 0.69 and \(-1.67\) m/s\({}^{2}\), and with a typical driver it varies between 0.68 and \(-1.67\) m/s\({}^{2}\). Figure 12 indicates that the variations in velocity are greater with sluggish and typical drivers. Figure 13 shows that for large potholes, with an aggressive driver, the acceleration decreases to \(-1.27\) m/s\({}^{2}\) at 57.5 s and increases to 0.59 m/s\({}^{2}\) at 77.0 s. It is approximately \(-1.67\) m/s\({}^{2}\) between 120.0 and 134.0 s. It is 0.67 m/s\({}^{2}\) at 156.0 s and \(-1.67\) m/s\({}^{2}\) at 194.5 s. With a sluggish driver, the acceleration decreases to \(-1.58\) m/s\({}^{2}\) at 54.5 s and then increases to approximately 0.64 m/s\({}^{2}\) between 77.0 s and 99.5 s. It is \(-1.67\) m/s\({}^{2}\) between 114.5 and 131.5 s and 0.67 m/s\({}^{2}\) between 151.5 and 183.5 s. The velocity then decreases to \(-1.67\) m/s\({}^{2}\) at 192.5 s. The acceleration with a typical driver is similar to that with a sluggish driver. Figure 10: Single vehicle acceleration for the ID model on a 1 km circular road with \(\delta=1.0,\ 4.0\), and 200. The time and space traffic flow behavior for the ID model on a 1 km circular road is presented in Figure 14. For \(\delta=1.0\), at 1.0 s the flow is zero and gradually increases to approximately 0.71 veh/s between 77.0 and 195.0 s. It is 0.70 veh/s at 198.5 s and 875.7 m, as shown in Figure 14a. At \(-\)123.2 m, the flow is 0.70 veh/s at 199.0 s. Between 279.7 and 689.3 m, it is approximately 0.52 veh/s and then increases to 0.70 veh/s at 875.7 m. For \(\delta=4.0\), Figure 14b shows that the flow is 0 at 0 s, increases to 3.70 veh/s at 73.0 s, and then varies between 12.28 and 0.37 veh/s from 99.5 to 200 s. For \(\delta=200\), the flow is 0 at 1.0 s and increases to 3.70 veh/s at 63.5 s. It varies between 14.59 and 0.30 veh/s from 84.0 s to  
Figure 11: Single vehicle acceleration for the proposed model on a 1 km circular road with small potholes. Figure 5:0 Single vehicle acceleration for the proposed model on a 1 km circular road with medium potholes. 200 s, as shown in Figure 14c. With \(\delta=4.0\) and 200, at 200 s the flow over space initially increases to a maximum and then drops to 0.30 veh/s. Figure 14 shows that with the ID model the variations in flow increase as \(\delta\) increases.