# Calibrating Microscopic Traffic Simulation Model Using Connected Vehicle Data and Genetic Algorithm
## 4 Results
### Calibration Results
\begin{table}
\begin{tabular}{c c c c c} \hline
**Errors in Time–Space** & **Before** & **After** & **\% of Change** & **Units** \\
**Diagrams** & **Calibration** & **Calibration** & **\%** & **\%** \\ \hline Mean & 208.53 & 178.94 & 14.19\% & m\(\cdot\)min \\ Median & 131.56 & 107.53 & 18.27\% & m\(\cdot\)min \\ Standard Deviation & 236.58 & 222.66 & 5.88\% & m\(\cdot\)min \\ Minimum & 3.14 & 1.66 & 47.14\% & m\(\cdot\)min \\ Maximum & 2249.19 & 2170.08 & 3.52\% & m\(\cdot\)min \\
25 th percentile & 34.22 & 32.42 & 5.27\% & m\(\cdot\)min \\
75 th percentile & 310.90 & 240.73 & 22.57\% & m\(\cdot\)min \\ Variance & 55,969.14 & 49,579.17 & 11.42\% & (m\(\cdot\)min)\({}^{2}\) \\ Skewness & 2.76 & 3.29 & \(-19.25\%\) & - \\ Kurtosis & 16.27 & 19.93 & \(-22.44\%\) & - \\ Coefficient of Variation & 1.13 & 1.24 & \(-9.68\%\) & - \\ \hline \end{tabular}
\end{table} 
Table 3: Statistical results of the errors in time–space diagrams before and after the calibration process. Figure 5: The results of the GA, showing the lowest median error across all populations for each generation. Percentile values give a deeper insight into the distribution of errors. The 25 th percentile saw a slight improvement (5.27%), indicating that lower error values are becoming more common. More substantial is the improvement in the 75 th percentile, decreasing from 310.90 to 240.73, showing that higher errors have been effectively reduced. Moreover, the variance decreased from 55,969.14 to 49,579.17, confirming a reduction in the spread of error data around the mean. Interestingly, the skewness and kurtosis increased from 2.76 to 3.29 and from 16.27 to 19.93, respectively, indicating that the distribution of errors has become more positively skewed and peaked post-calibration. A slight increase in variability, as indicated by kurtosis, points to remaining outlier cases that need further investigation. Lastly, the coefficient of variation increased from 1.13 to 1.24. This increase indicates a higher relative variability in error distribution relative to the mean after calibration, which suggests variability in the effectiveness of the calibration across different cases. Overall, the alignment between the simulated and ground truth trajectories has improved, as evidenced by the decrease in the mean and median errors. These measures show the simulation model's overall accuracy as well as its primary tendency. The observed drop in the mean error can be attributed to the calibration's successful reduction in bigger  
Figure 6: Time–space diagrams before (**a**) and after (**b**) the calibration process, highlighting error reduction. discrepancies, as indicated by the decrease in the 75 th percentile error. This suggests that high-error instances were effectively handled by the calibration framework, resulting in a more realistic simulation. When compared to similar research [21; 29], the method presented in this study performed better. The increase in kurtosis and skewness indicates that although overall errors decreased, the distribution of errors became more positively skewed and peaked. This suggests that there are now fewer but more significant outliers and a greater percentage of errors are concentrated closer to the bottom end of the distribution. These outliers likely reflect specific traffic situations, such as highly congested segments or complex merging and lane-changing behaviors, that were not fully captured during the calibration process. Furthermore, the higher relative variability in the error distribution, as reflected in the coefficient of variation, indicates that although the calibration enhanced average performance, its efficacy varied depending on traffic conditions. This variability may stem from the limitations of the selected model parameters, which might not fully account for certain driver behaviors unique to the selected highway segment. For example, local driving patterns, such as aggressive merging or braking, may not have been adequately represented in the calibration dataset.