## 4 Example Demonstration
### Model Evaluation Results  
The samples are fed into the LSTM, GRU, 1 DCNN, and 1 DCNN plus GRU models for training. The loss functions of the training and validation sets are obtained by training, as shown in Figure 5, where (a) shows that the loss function of the training set of each model gradually decreases and eventually stabilizes with the increase in the number of iterations. The loss function of the validation set in (b) gradually decreases with the increasing number of iterations. Although all fluctuate, the 1 DCNN model fluctuates the most. Thus, it can be concluded that the 1 DCNN model applied to the data of this thesis has a large error.  
In this paper, a 1 DCNN plus GRU model considering temporal and spatial characteristics, a GRU and LSTM model considering temporal characteristics, and a 1 DCNN model considering spatial characteristics were set up for experimental comparison. The results can be used to verify the highway toll station space-time characteristics of the impacts of traffic. A comparison of Tables 3 and 4 reveals that the 1 DCNN plus GRU model with spatio-temporal characteristics considered was 3.94% lower in the MAE, 1.12% lower in the RMSE, and 16.05 s longer in computing time than the LSTM model without spatio-temporal characteristics for predicting less traffic at toll station 17. The MAE was reduced by 4.10%, the RMSE was reduced by 1.57%, and the computing time was increased by 15.75 s compared to the GRU model for predicting traffic at toll station 17.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Name of the Parameter** & **Parameter Value** \\ \hline GRU & Hidden Layer & GRU(20) + GRU(10) \\  & B/E/Optimizer & 64/50/[PERSON] \\ \hline LSTM & Hidden Layer & LSTM(20) + LSTM(10) \\  & B/E/Optimizer & 64/50/[PERSON] \\ \hline
1 DCNN + GRU & Hidden Layer & Dense(128) + Conv1d(32) + Maxpooling1d + Conv1d(16) + Maxpooling + GRU(20) \\  & & + GRU(10) + Dense(10) \\  & B/E/Optimizer & 64/50/[PERSON] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Example of toll station flow data.  
Figure 5: Loss function diagram. (**a**) Training set loss function. (**b**) Validation set loss function.  
A comparison of Tables 3 and 4 reveals that the 1 DCNN plus GRU model with spatio-temporal characteristics considered had a 14.06% reduction in the MAE, 12.78% reduction in the RMSE, and 15.34 s increase in computing time compared to the LSTM model that did not consider spatio-temporal characteristics in predicting higher traffic volumes at toll booth 3. In comparison with the GRU model, the MAE decreased by 14.81%, the RMSE decreased by 13.58%, and the computing time increased by 14.64 s when predicting toll station 17.  
The prediction accuracy is relatively low due to the small total volume of traffic at toll station 17 and the large fluctuation of real traffic data, as shown in Figure 6a. By comparing the LSTM and GRU models that only considered the temporal characteristics, we can find that the 1 DCNN plus GRU can explore the spatial and temporal characteristics of toll station traffic more deeply and reduce the prediction error. The total volume of traffic at toll station 3 is relatively large. The model prediction effect is obviously improved.