# Prediction of Vacant Parking Spaces in Multiple Parking Lots: A DWT-ConvGRU-BRC Model
## 4 Experimental Results
### Results and Analysis
To illustrate the ability of the proposed model to predict the actual number of VPSs, in Table 3, we present a detailed comparison between the actual and predicted number of St7 parking lot VPSs (from 10:00 to 11:00, 6 May 2021) output by the proposed DWT-ConvGRU-BRC model. We also calculate the MAE, MAPE, and RMSE values for the time period. The output values of the DWT-ConvGRU-BRC model are very close to the real values. In addition, model performance evaluation should consider both prediction accuracy and time consumption. Table 4 compares the running times per round of the LSTM, GRU, ConvGRU, ConvLSTM, dConvLSTM-DN, DWT-ConvGRU, and DWT-ConvGRU-BRC models. The DWT-ConvGRU-BRC model considers the effects of factors such as wavelet noise reduction and external factors, so it is slightly inferior to the models that do not consider these factors in terms of running speed, but compared to the dConvLSTM-DN model proposed in [36], our model shows a significant improvement in running speed. In conclusion, our proposed model not only improves the effectiveness of predictions but also improves the running speed. \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}{*}{ConvGRU} & RMSE & 7.14 & 10.46 & 14.41 & 17.83 & 21.73 \\  & MAE & 4.74 & 7.25 & 10.01 & 12.31 & 14.59 \\  & MAPE(\%) & 1.01 & 1.51 & 2.08 & 2.62 & 3.16 \\  & RMSE & 7.70 & 10.55 & 14.28 & 16.87 & 20.01 \\ \multirow{4}{*}{ConvLSTM} & MAE & 5.15 & 7.30 & 9.91 & 11.45 & 13.14 \\  & MAPE(\%) & 1.09 & 1.54 & 2.07 & 2.35 & 2.73 \\  & RMSE & 7.23 & 10.75 & 15.10 & 17.88 & 19.43 \\ \multirow{4}{*}{dConvLSTM-DCN} & MAE & 4.98 & 7.36 & 10.18 & 11.77 & 13.02 \\  & MAPE(\%) & 1.04 & 1.53 & 2.11 & 2.47 & 2.68 \\ \multirow{4}{*}{DWT-ConvGRU} & RMSE & 5.2 & 6.99 & 12.14 & 16.9 & 21.4 \\  & MAE & 3.66 & 4.99 & 8.42 & 11.54 & 14.03 \\ \multirow{4}{*}{DWT-ConvGRU} & MAE(\%) & 0.79 & 1.1 & 1.83 & 2.57 & 2.96 \\  & RMSE & 5.07 & 6.49 & 10.44 & 15.33 & 19.35 \\ \multirow{4}{*}{DWT-ConvGRU-BRC} & MAE & 3.6 & 4.65 & 7.41 & 10.58 & 12.89 \\  & MAPE(\%) & 0.78 & 0.97 & 1.56 & 2.26 & 2.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Time** & **Real** & \multicolumn{5}{c}{**Predicted Values**} \\ \hline
**Point** & **Value** & **5 min** & **15 min** & **30 min** & **45 min** & **60 min** \\ \hline
6 May 2021 10:00 & 652 & 647 & 643 & 654 & 674 & 669 \\
6 May 2021 10:05 & 652 & 645 & 639 & 643 & 667 & 661 \\
6 May 2021 10:10 & 644 & 646 & 636 & 632 & 659 & 655 \\
6 May 2021 10:15 & 641 & 642 & 633 & 620 & 648 & 645 \\
6 May 2021 10:20 & 643 & 641 & 632 & 622 & 637 & 636 \\
6 May 2021 10:25 & 639 & 641 & 629 & 617 & 625 & 626 \\
6 May 2021 10:30 & 638 & 642 & 625 & 614 & 611 & 615 \\
6 May 2021 10:35 & 628 & 632 & 624 & 615 & 597 & 604 \\
6 May 2021 10:40 & 615 & 623 & 624 & 606 & 593 & 591 \\
6 May 2021 10:45 & 609 & 613 & 616 & 605 & 587 & 578 \\
6 May 2021 10:50 & 603 & 600 & 606 & 605 & 582 & 564 \\
6 May 2021 11:05 & 594 & 594 & 596 & 605 & 582 & 557 \\
6 May 2021 11:00 & 584 & 584 & 585 & 591 & 575 & 554 \\ MAE & & 3.23 & 7.54 & 12.08 & 17.15 & 20.69 \\ MAPE(\%) & & 0.51 & 1.19 & 1.91 & 2.74 & 3.36 \\ RMSE & & 4.01 & 8.45 & 14.17 & 18.69 & 23.46 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparisons between the real and predicted numbers of VPSs at the St7 parking lot.