## 4 Numerical Experiment  
In this section, we investigate the influence of police enforcement crowdsourced data from navigation apps on traffic speed in The Netherlands. We selected corridors that met two conditions: (a) there are both police speed enforcement records and speed loop detectors; and (b) the number of speed cameras on the corridor is relatively small to ensure that the reports are all about police activity. Two datasets, namely, the speed dataset and the crowdsourced dataset of The Netherlands, are used in our experiment:  
* The speed data are provided by the national data warehouse for traffic information ([[http://opendata.ndw.nu/](http://opendata.ndw.nu/)]([http://opendata.ndw.nu/](http://opendata.ndw.nu/)), accessed on 26 October 2023). The raw speed data are collected from loop detectors on the highways every 5 min interval, and the samples are shown in Table 1.
* The crowdsourced data of police speed enforcement reported between September and December 2021 in The Netherlands are provided by a navigation app. The dataset includes the latitude, longitude, and start and end time information reported by users on the navigation apps, and a sample of the data is provided in Table 2. Erroneous reports were removed, and reported police activities were accurately mapped to specific road segments using their location information. Figure 5 shows the study area and the location of speed loop detectors and reported police activities. Figure 4: The internal unit of GCN-GRU. A section of the A67 highway on the south of Eindhoven from west to east was investigated first. It is a two-lane highway and the speed limit on express lane is 120 [km/h] and on the local lane is 100 [km/h]. There are two speed check points in this section. We collected the historical traffic speed data of the past 7 days for every 5 min interval of each check time period. The speed data are all from local lanes since there are plenty of missing \begin{table}
\begin{tabular}{l l l l l l l} \hline
**ID** & **Created\_at** & **Updated\_at** & **Latitude** & **Longitude** & **Highway** & **Location** \\ \hline
**1** & 2021-11-08 15:06 & 2021-11-08 16:14 & 51.3699 & 5.52383 & A2 & Valkenswaard \\
**2** & 2021-09-10 06:04 & 2021-09-10 06:42 & 51.37228406 & 5.521841 & A2 & Valkenswaard \\
**3** & 2021-09-11 11:36 & 2021-09-11 14:38 & 51.37074803 & 5.523306 & A2 & Valkenswaard \\
**4** & 2021-09-10 05:15 & 2021-09-10 05:21 & 51.36998451 & 5.524018 & A2 & Valkenswaard \\
**5** & 2021-09-14 19:31 & 2021-09-15 03:55 & 51.36921362 & 5.524737 & A2 & Valkenswaard \\
6 & 2021-09-09 05:53 & 2021-09-09 06:52 & 51.36845498 & 5.525459 & A2 & Valkenswaard \\... & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 2: Sample of speed check data. Figure 5: Study area. data from loop detectors on express lanes. Then, we make predictions by the GCN-GRU model for each point and its corresponding inspection time; 80% of the input data was used as the training set and the remaining 20% was used as the testing set. Figure 6 shows the predicted and actual speeds during the reported police enforcement periods and an hour before the start of police enforcement as a comparison. We performed the one factor analysis of variance (ANOVA) test to determine whether there are any statistically significant differences between the means of the predicted and actual speeds. In addition, in order to compare the performance of the GCN-GRU model in predicting traffic speed during the periods with and without police enforcement, three evaluation indicators were used:  
1. Mean absolute error (MAE): \[MAE=\frac{1}{n}\sum_{i=1}^{n}\left|Y_{t}-\hat{Y}_{t}\right|,\] (6)
2. Root mean square error (RMSE): \[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(Y_{t}-\hat{Y}_{t})^{2}},\] (7)
3. Accuracy (ACC): \[ACC=1-\frac{\left\|Y-\hat{Y}\right\|_{F}}{\left\|Y\right\|_{F}},\] (8) where \(\hat{Y}_{t}\) represents the actual traffic speed at time \(t\), \(Y_{t}\) represents the predicted speed, \(n\) is the total number of test samples, and \(\left\|.\right\|_{F}\) represents the Frobenius norm.