## 7 Validation of Simulation Results
### Combined Speed Accuracy Score Metric  
Tables 3 and 4 present the results of four simulation scenarios for SD_02 and SD_07 detectors. They provide key insights into the effectiveness of modeling synthetic speed data compared to real data. For SD_02, the highest CSAS value (80.2 for sim_1) results from the excellent percentage agreement of 50 km/h exceedances (61.2%) and moderate RMSE (11.8 km/h), indicating a balanced representation of the tendency to exceed limits, which may support decisions to strengthen enforcement in sensitive areas such as school zones. For SD_07, sim_3 achieves the highest average speed accuracy (56.1 km/h vs. 56.6 km/h actual), with CSAS 79.7, suggesting better adaptation to transit traffic, which implies the potential usefulness of this configuration in optimizing speed limits on roads with higher traffic volumes. Differences in RMSE (e.g., 13.9 for sim_4 in SD_02 vs. 14.1 for sim_4 in SD_07) indicate greater variance in the modeling of individual speeds, highlighting the need for further calibration of parameters such as speedFactor to improve simulation  
fidelity. These analytical implications suggest that the choice of the optimal scenario should depend on the specific characteristics of the area, and the results can inform prevention strategies, such as adjusting police patrols or road infrastructure to local risk patterns. In contrast, RMSE measures overall prediction error without focusing on specific speed thresholds. However, the RMSE is also essential when one is concerned with accurately representing high speeds (e.g., whether a vehicle traveling 60 km/h is predicted as 55 km/h or 45 km/h), which affects the nature of traffic and its safety. Therefore, it cannot be ignored in the evaluation of synthetic data and should be treated as an essential auxiliary metric. It can also, together with the percentage concordance, be used to create a new metric to select the best simulation scenario explicitly. A new and proprietary CSAS metric called Combined Speed Accuracy Score was proposed and included in the compilations, which combines the folowing:  
* Percentage compliance (0-100% value). * Normalized RMSE (scaled to 0-100 range based on speed scale). * Additional weights for differences in percentages above speed limits 1 (SL1) and 2 (SL2) emphasize the priority of propensity to exceed limits. The CSAS metric is calculated from the relationship (1)  
\[ \begin{array}{c}\text{CSAS}=\text{w}_{1}\cdot\text{C}+\text{w}_{2}\cdot(100- \text{NRMSE})+\\ +\text{w}_{3}\cdot\left(100-\left|\text{P}_{>\text{SL1}}^{\text{real}}-\text{P} _{>\text{SL1}}^{\text{sim}}\right|\right)+\text{w}_{4}\cdot\left(100-\left| \text{P}_{>\text{SL2}}^{\text{real}}-\text{P}_{>\text{SL2}}^{\text{sim}}\right|\right) \end{array}  \tag{1}\]  
The normalized RMSE is calculated from the relationship (2)  
\[\text{NRMSE}=\left(\frac{\text{RMSE}}{100}\right)\cdot 100 \tag{2}\]  
where  
* C--Conformity percentage (%);
* NRMSE--Normalized Root Mean Squared Error;
* preal > SL1--Percentage of vehicles exceeding Speed Limit 1 for real data (%);
* psim > SL1--Percentage of vehicles exceeding Speed Limit 1 for simulated data (%);
* preal > SL2--Percentage of vehicles exceeding Speed Limit 2 for real data (%);
* psim > SL2--Percentage of vehicles exceeding Speed Limit 2 for simulated data (%);
* w1, w2, w3, w4--Weights, set, e.g., to w1 = 0.2, w2 = 0.15, w3 = 0.2, w4 = 0.3. The weights used in the CSAS metric were selected based on this study's priorities. The primary focus is on modeling the propensity to exceed speed limits, which is crucial for predicting road hazards. The highest weight, w4 = 0.3, describing the percentage difference in SL2 violations, reflects the greater risk associated with higher speeds. WHO data and accident impact analyses confirm this. The weight w3 = 0.2 for SL1 accounts for the importance of lower limits in sensitive areas, such as school zones. In contrast, w1 = 0.2 ensures the overall balance of speed distribution compliance.