## 4 Numerical Experiment
MAE and RMSE can well reflect the deviation between the predicted values and the actual  
Figure 6: The predicted and actual speeds on the A67 highway. The shaded area shows the enforcement period. values, and smaller values of them indicate better prediction. ACC is used to detect the prediction precision, and larger values represent better prediction. Table 3 shows the test results of the A67 highway. A one-factor ANOVA test with a significance level of 0.05 is performed. The \(p\)-values of the groups with and without police enforcement are 0.1502 and 0.2289, respectively, which means that the differences between the actual and predicted speed means are not statistically significant. Comparing the prediction evaluation indicators of the model with and without police enforcement shows that the model performs slightly better when there is no enforcement. We note that there are only two speed check points on this corridor, and relatively small samples might be the reason for not seeing a statistically significant difference. However, the actual average speed is 1 [km/h] lower than the predicted average speed during the police enforcement periods, while it is slightly higher when no police enforcement is reported. Then, we selected a section of A2, one of the busiest highways in The Netherlands. This section is located in the south of Eindhoven, and connects Eindhoven to Weert. We first analyzed the south-to-north driving direction on A2. It is a two-lane highway, and the speed limit is again 120 [km/h] on the express lane and 100 [km/h] on the local lane. According to the latitude and longitude information of police enforcement, there are eight enforcement points distributed in this direction. Among them, the speed check at two locations occurred during weekends, when the speed datasets had a large amount of missing data, so they were not considered for the analysis. Again, the speed data were collected from local lanes. The predicted and actual speeds with and without police enforcement are shown in Figure 7. The ANOVA test results and the prediction performance of GCN-GRU on this corridor are reported in Table 4. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**With Police**} & & & & & & \\ \hline
**Groups** & **Count** & **Average** & **F** & \(p\)**-Value** & **MAE** & **RMSE** & **ACC** \\ \hline Prediction value & 48 & 96.93 & 4.8102 & 0.0308 & 3.4016 & 4.6643 & 0.9553 \\ Actual value & 48 & 94.56 & & & & & \\ \hline
**Without Police** & & & & & & & \\ \hline
**Groups** & **Count** & **Average** & **F** & \(p\)**-Value** & **MAE** & **RMSE** & **ACC** \\ \hline Prediction value & 74 & 95.79 & & & & & \\ Actual value & 74 & 96.46 & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The test results of A2 highway for the south-to-north driving direction. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Groups** & **Count** & **Average** & **F** & \(p\)**-Value** & **MAE** & **RMSE** & **ACC** \\ \hline Prediction value & 9 & 90.59 & & & & & \\ Actual value & 9 & 89.59 & & & & & \\ \hline
**Without Police** & & & & & & & \\ \hline
**Groups** & **Count** & **Average** & **F** & \(p\)**-Value** & **MAE** & **RMSE** & **ACC** \\ \hline Prediction value & 36 & 91.09 & & & & & \\ Actual value & 36 & 91.55 & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The test result of the A67 highway. It can be seen from Table 4 that the \(p\)-value of the with-police group (=0.03) is smaller than the confidence level 0.05, which means that the predicted and the actual speeds have statistically significant differences. On the contrary, no significant differences between the predicted and actual speeds were observed during the time period one hour before the police enforcement. Similar to the A67 corridor, in the presence of the police, the average of the actual speed is smaller than the predicted speed by 2.37 [km/h]; however, the actual average is 0.67 [km/h] larger than the predicted average when there is no police enforcement.