# Simulation-Oriented Analysis and Modeling of
## 5 Model Calibration
### Model Performance at the Population Level  
Introducing distraction parameters has improved the calibration accuracy of IDM-distraction by an average of 7.14% compared with IDM, as demonstrated in Figure 3. Specifically, on expressways with high traffic volume, the model accuracy for mild distraction in IDM-distraction showed the most significant improvement, with an increase of 18.8% compared to IDM. The accuracy for excessive and moderate distractions also saw \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{3}{c}{**Expressway with Low Traffic**} & \multicolumn{3}{c}{**SURFACE ROAD**} \\  & \multicolumn{2}{c}{**Volume**} & \multicolumn{3}{c}{**Volume**} & \multicolumn{3}{c}{**Volume**} & \multicolumn{3}{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 & 0.585 & 0.275 & 1.080 & 0.494 & 0.144 & 0.822 & 0.237 & 0.658 \\ \(a_{cmf}^{(n)}\) & 0.906 & 1.828 & 0.716 & 5.000 & 0.840 & 2.966 & 1.311 & 2.000 & 0.973 \\ \(\widetilde{V}_{n}(t)\) & 30.638 & 25.467 & 23.795 & 32.016 & 29.605 & 27.007 & 25.292 & 23.115 & 18.793 \\  & **GMM** & **GMM** & **GMM** & **GMM** & **GMM** & **GMM** \\  & \(\mu=[4.09,\) & \(\mu=[4.62,\) & \(\mu=[1.68,\) & \(\mu=[3.93,\) & \(\alpha\_stable\) & \\  & 1.58], & **Normal** & 0.94], & **Normal** & 4.11], & 1.42], & **Normal** & \(\alpha=0.40\), & **Normal** \\ \(\tau\) & \(\sigma=[0.18,\) & \(\mu=2.77,\) & \(\sigma=[0.04,\) & \(\mu=2.46,\) & \(\sigma=[0.73,\) & \(\sigma=[0.39,\) & \(\mu=3.28,\) & \(\beta=-0.99,\) & \(\mu=3.28,\) \\  & 1.13], & \(\sigma=1.53\) & 0.48], & \(\sigma=[1.53\) & 0.33], & 0.71], & \(\sigma=1.66\) & \(\gamma=0.76\), & \(\sigma=1.66\) \\  & \(\alpha=[0.50,\) & \(\alpha=[0.17,\) & \(\alpha=[0.65,\) & \(\alpha=[0.56,\) & & \(\delta=4.49\) & \\  & 0.50] & & 0.83] & & 0.35] & 0.44] & \\  & **GMM** & **GMM** & **GMM** & **GMM** & **GMM** & **GMM** \\  & & \(\mu=[8.33,\) & \(\mu=[15.32,\) & \(\mu=[8.10,\) & \(\mu=[12.72,\) & \(\alpha\_stable\) & \(\alpha\_stable\) & \(\alpha\_stable\) \\  & \(-14.39], & **Normal** & \(-6.51,\) & \(-11.03,\) & \(-5.71,\) & \(\alpha=[1.41,\) & \(\alpha=1.58,\) & \(\alpha=2,\) \\ \(\theta\) & \(\mu=0.11,\) & \(\sigma=[24.98,\) & \(\mu=-1.43,\) & \(\sigma=[49.69,\) & \(\sigma=[22.57,\) & \(\sigma=[62.08,\) & \(\beta=-0.74,\) & \(\beta=-0.67,\) & \(\beta=0.94,\) \\  & \(\sigma=13.53\) & \(22.18], & \(\sigma=10.57\) & \(22.57,\) & \(\sigma=[49.69],\) & \(18.17,\) & \(\gamma=3.80,\) & \(\gamma=4.21,\) & \(\gamma=8.01,\) \\  & & \(\alpha=[0.64,\) & \(\alpha=[59.62,\) & \(\alpha=[0.43,\) & \(\alpha=[0.32,\) & \(\delta=0.42,\) & \(\delta=-2.09\) & \(\delta=-2.00\) \\  & & 0.36] & & 12.11] & 0.57] & 0.68] & \\  & & **GMM** & **GMM** & **GMM** & **GMM** & **GMM** & & \\  & \(\alpha\_stable\) & \(\mu=[3.75,\) & \(\alpha\_stable\) & \(\mu=[3.17,\) & \(\mu=[-0.86,\) & \(\mu=[0.49,\) & \(\mu=[5,\) & \(\alpha\_stable\) & \(\alpha\_stable\) \\  & \(\alpha=0.40,\) & \(-3.68], & \(\alpha=0.4,\) & \(-3.15], & \(-5], & \(-2.16,\) & \(\alpha=2,\) & \(\alpha=0.4,\) \\ \(\lambda\) & \(\beta=0.47,\) & \(\sigma=[0.08,\) & \(\beta=0.96,\) & \(\sigma=[0.14,\) & \(\sigma=[2.27,\) & \(\sigma=[2.27,\) & \(\sigma=[0,\) & \(\beta=-0.97,\) & \(\beta=-0.38,\) \\  & \(\gamma=0.04,\) & \(\sigma=[0.04],\) & \(\gamma=1.01,\) & \(0.20], & \(\sigma=[0.01,\) & \(\sigma=[0.01,\) & \(\sigma=[0,\) & \(\beta=-0.97,\) & \(\gamma=0.46,\) \\  & \(\delta=-0.09\) & \(\alpha=[0.64,\) & \(\delta=-3.14\) & \(\alpha=[0.45,\) & \(\alpha=[0.45,\) & \(\alpha=[0.63,\) & \(\alpha=[0.95,\) & \(\alpha=[0.26,\) & \(\delta=0.75\) & \(\delta=2.22\) \\  & 0.36] & & 0.55] & 0.37] & 0.05] & 0.42, 0.32] & \\ \hline \hline \end{tabular}
\end{table}