## 7 Validation of Simulation Results  
Any model created by machine learning will be as good as the data on which it was trained. This principle should also be kept in mind when producing synthetic data for the concept of a systemic solution for area-based vehicle speed control. In the validation process, data from actual vehicle speed measurements on the simulated area of the road network are beneficial. This is what the preliminary field studies carried out initially served to do: to obtain real data. And this is how the term \"good data\" should be understood in this case. The data was collected systematically, within a defined time frame, and under consistent weather conditions. The actual data were then matched with the results of a series of simulations. Four simulation scenarios and data for two speed detectors, SD_02 and SD_07, were selected for validation and presentation of results. Figure 10 presents a graphical comparison of actual speed distributions (measured in the field using SD_02 and SD_07 detectors) with the results of four simulation scenarios (sim_1, sim_2, sim_3, and sim_4) carried out in the SUMO software for the exact locations in the municipality of Stare Babice. The graphs show density curves. They illustrate how well the simulations reproduce actual speed patterns, taking into account speed limits (40 km/h for SD_02 and 50 km/h for SD_07). The significance of this figure lies in the validation of the simulation model. It allows us to assess which scenario most accurately reproduces the actual data, which is crucial for the reliability of generating synthetic data for hazard prediction. Differences in distributions, such as shifts in average speeds or dispersion of limit violations, indicate the need to calibrate parameters (e.g., speedFactor and driver profiles). Their analysis supports decisions on the optimal configuration of the speed control system, for example, in areas with a high risk of accidents. Histograms of the distributions of the actual velocities (measured during testing) and the velocities obtained from each simulation scenario for the SD_02 and SD_07 detectors are shown in Figures 11 and 12, respectively. Figure 11: Comparison of actual velocity distributions with results of individual simulations for the SD_02 detector (source: own development). Figure 10: Comparison of actual velocity distributions with results of four simulations for SD_02 and SD_07 detectors (source: own elaboration). Both figures illustrate trends in actual and simulated speed distributions for SD_02 and SD_07 detectors. For SD_02, sim_1 exhibits a trend of speed concentration above 50 km/h, similar to the actual value (61.2%), indicating good calibration of aggressive driver profiles--meanwhile, sim_2 underestimates (48.0%), indicating overly conservative speedFactor assumptions. For SD_07, sim_3 exhibits a symmetrical trend, with an increase in 50 km/h violations (72.7%), which better reflects transit traffic. These trends suggest that the higher CSAS in sim_1 (80.2 for SD_02) is due to better risk representation. This may help support traffic management through dynamic speed limits in school areas (SD_02) or optimizing the number of police patrols in transit (SD_07). A comparison of the velocity distributions for all simulation scenarios with actual data for the SD_02 and SD_07 detectors is shown in Figures 13 and 14, respectively. Figure 12: Comparison of actual velocity distributions with results of individual simulations for the SD_07 detector (source: own development). Figure 13: Comparison of velocity distributions of all simulation scenarios with real data for the SD_02 detector (source: own development). The numerical values of the results from the four simulation scenarios, along with the determination of the percentage of agreement with the actual data and the calculation of the RMSE (mean-square error) for the SD_02 and SD_07 detectors, are presented in Tables 3 and 4, respectively.