# Prediction of Vacant Parking Spaces in Multiple Parking Lots: A DWT-ConvGRU-BRC Model
## 4 Experimental Results
### Results and Analysis  
Fifty experiments were carried out, and the mean was selected as the result to improve the statistical significance of the difference in precision. Table 1 shows the detailed RMSE, MAE, and MAPE data for our DWT-ConvGRU-BRC model. Figure 9 shows the effect of the DWT-ConvGRU-BRC model in the Lot1, St5, and St7 parking lots for 5, 15, 30, 45, and 60 min VPS predictions, where the x-axis represents the time interval, and the y-axis represents the number of VPSs. Our model is robust in predicting the availability of VPSs in multiple parking lots. From Section 3, we conclude that parking occupancy is affected by external factors such as weather. This is consistent with the conclusions drawn in [33; 34; 35; 38; 39]. Therefore, we performed ablation experiments in Table 1 to compare the effect of the presence or absence of external factors on VPS prediction. We find that the inclusion of external factors such as temperature, wind speed, weekdays, and weekends was beneficial in improving the accuracy of the forecasts. For the RMSE, MAE, and MAPE, the forecasting models with external factors outperformed those without external factors in 40, 35, and 39 of the 55 forecasting tasks, respectively. This shows that considering external factors can improve the accuracy of VPS prediction, so it can be said that external factors have a significant  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**DWT-ConvGRU-BRC**} & \multicolumn{6}{c}{**DWT-ConvGRU-BRC**} \\  & & \multicolumn{6}{c}{**without External Factors**} & \multicolumn{6}{c}{**with External Factors**} \\ \cline{3-11}  & & **5 min** & **15 min** & **30 min** & **45 min** & **60 min** & **5 min** & **15 min** & **30 min** & **45 min** & **60 min** \\ \hline RMSE & St1 & 2.87 & 4.59 & 5.55 & 8.10 & 9.4  
impact on parking prediction. Figure 10 specifically shows the prediction effect of our proposed DWT-ConvGRU-BRC model for each parking lot. It can be seen from the figure that our model has good timeliness in predicting the number of VPSs in multiple parking lots, and it is relatively robust to changes in the spatial-temporal correlation of VPSs and can accurately achieve predictions. As some models can only predict for a single parking lot, we compared the effectiveness of these models in predicting the number of VPSs at 5, 15, 30, 45, and 60 min, using the St7 parking lot as an example. The LSTM and GRU models can effectively extract temporal information from nonlinear time series data, but they fail to consider the spatial correlation between parking lots within a region. The ConvGRU model outperforms the ConvLSTM model in terms of running speed while capturing spatial-temporal correlations. After wavelet noise reduction, the forecasts improved significantly, and external factors, such as weather, improved the accuracy of the long-term forecasts. As illustrated in Table 2, the proposed DWT-ConvGRU-BRC model is significantly superior to the benchmark methods. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Indicator** & **5 min** & **15 min** & **30 min** & **45 min** & **60 min** \\ \hline \multirow{4}{*}{LSTM} & RMSE & 14.86 & 17.14 & 20.84 & 29.24 & 34.45 \\  & MAE & 8.54 & 11.07 & 14.92 & 26.71 & 33.12 \\  & MAPE(\%) & 1.32 & 1.72 & 2.31 & 4.15 & 5.17 \\ \cline{1-1}  & RMSE & 10.41 & 13.86 & 18.75 & 23.42 & 29.54 \\ \cline{1-1}  & MAE & 7.80 & 11.40 & 15.15 & 19.25 & 21.74 \\ \cline{1-1}  & MAPE(\%) & 1.57 & 2.50 & 2.93 & 4.36 & 5.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of operating results. Figure 10: DWT-ConvGRU-BRC model evaluation metrics for each parking lot. (**a**) RMSE; (**b**) MAE; (**c**) MAPE. Figure 9: Comparison between the DWT-ConvGRU-BRC prediction and actual values at 5, 15, 30, 45, and 60 min. (**a**) St5 parking lot; (**b**) St7 parking lot; (**c**) Lot1 parking lot.