# Simulation-Oriented Analysis and Modeling of
## 5 Model Calibration
### Model Performance at the Population Level

Table 4: Bounds and initial searching values of Intelligent Driver Model (IDM) parameters. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Scenarios**} & \multicolumn{2}{c}{**Expressway with High Traffic**} & \multicolumn{2}{c}{**Expressway with Low Traffic**} & \multicolumn{2}{c}{**SURFACE ROAD**} \\  & \multicolumn{2}{c}{**Volume**} & \multicolumn{2}{c}{**Volume**} & \multicolumn{2}{c}{**Total**} \\ \hline
**Pattern** & **Excessive** & **Moderate** & **Mild** & **Excessive** & **Moderate** & **Mild** & **Excessive** & **Moderate** & **Mild** \\ \hline \(S_{jam}^{(n)}\) & 3.614 & 3.745 & 2.663 & 2.974 & 0.911 & 3.854 & 2.103 & 6.074 & 6.840 \\ \(\widetilde{V}_{n}(t)\) & 0.671 & 0.437 & 1.223 & 0.814 & 0.875 & 0.621 & 0.886 & 0.140 & 1.032 \\ \(a_{max}^{(n)}\) & 0.917 improvements. On surface roads, IDM-distraction achieved the highest model accuracy for moderate distraction, with a 9.7% increase compared to IDM. Although the performance of the two models under excessive and mild distraction patterns is similar, IDM-distraction slightly outperforms IDM. On expressways with low traffic volume, IDM-distraction exhibited lower RMSNE values for both excessive and mild distraction patterns, indicating better accuracy in these environments. However, for moderate distraction, the accuracy of IDM-distraction was slightly lower than that of IDM. This may be due to the moderate distraction pattern representing a \"gray area\" where drivers' behaviors become more unpredictable. As illustrated in Figure 2c, the standard deviation of speed for drivers under moderate distraction is significantly larger on expressways with low traffic volume, and the ranges for maximum acceleration and deceleration are also significantly broader compared to other traffic conditions and distraction patterns. Based on Figure 4, we can analyze the distribution of the three distraction parameters. (1) Reaction times  
Firstly, on expressways with high traffic volume, drivers experiencing excessive distraction have significantly prolonged reaction times compared to the other two distraction patterns. In contrast, on expressways with low traffic volume, the differences in reaction times among the three distraction patterns are minor, suggesting that low traffic volume has a smaller impact on distracted driving behaviors. On surface roads, reaction times are longer across all three distraction patterns, likely because the complex environment of surface roads increases driver workload, requiring more time to respond to emergencies when distracted. (2) Differences in speed perception  
Regarding the differences in speed perception, whether on expressways with high or low traffic volumes, the distribution under different distraction patterns is similar, indicating that traffic volume has a lesser impact on drivers' speed perception on expressways. However, on surface roads, the distribution of speed perception deviation is broader among excessively distracted drivers, suggesting that these drivers are more prone to extreme perception deviations. (3) Deviation in the perception of following distance  
Excessively distracted drivers exhibit noticeable perception biases regarding following distance both on expressways with low traffic volume and on surface roads. This indicates that excessive distraction leads to greater perceptual deviation in following distance, affecting vehicle control. The distribution of perception deviation under moderate distraction is wider than under mild distraction, indicating more extreme values and thus more unstable  
Figure 3: GA parameter-setting results for IDM and IDM-distraction models. perceptual abilities. On expressways with low traffic volume, perception deviation of following distance for excessive distraction is larger, while it is smaller for mild distraction. This shows that the more severe the distraction pattern in low traffic conditions is, the greater is its impact on distance perception deviation.