# Augmentation of Deep Learning Models for Multistep Traffic Speed Prediction
## 4 Results Analysis and Discussion  
Different baseline models were used in traffic forecasting problems, such as ARIMA and Kalman filter. In this study, ARIMA and Kalman filter methods are not compared, as the performances of these models are far behind, based on our literature review [42]. In this study, we compared and evaluated the performance of our proposed model, AttBDLSTM-FCN, with different state-of-the-art baseline models, e.g., fully convolutional network (FCN) [38], LSTM [3], GRU NN [4], LSTM with fully connected deep neural network layer (LSTM-DNN) [43,44], LSTM with fully convolutional network (LSTM-FCN) [35,45], and BDLSTM [46]. We also examined and evaluated the performance of baseline models with a different number of time lags (time frames) studied in this paper, such as time lags of 3, 6, and 12, respectively. After conducting comprehensive research, we learned that the compared models performed well on small time lags as the time lags (time frames) increased, and their performance decreased. The GRU model showed its best performance when it used six time lags together. The MAE and MAPE were 1.80 and 3.69%, respectively. As the time lags increased onward, the performance of the GRU model decreased accordingly. In the case of LSTM, when the time lag was set to greater than six, its performance started deceasing, accordingly. The best results of LSTM models were 1.74 and 3.90% MAE and MAPE, respectively, when it used six time lags as input. By adding a DNN layer in the LSTM model, the performance of the model was enhanced, and the error was reduced to 1.86 and 4.45% MAE and MAPE, respectively. LSTM-DNN models also outperformed when the time lag was set as three. By increasing the time lags from three onward, the model performance decreased, and the error rate increased. In nonhybrid models, the BDLSTM model outperformed other baseline models such as GRU, LSTM, and LSTM-DNN. The BDLSTM model also showed consistent behavior with the LSTM-DNN model discussed above. It had its best performance when the time lag was set as three. The MAE and MAPE were reduced to 1.40 and 2.99%, respectively. In hybrid models, the LSTM-FCN showed the best performance when it used six time lags together as input; the MAE and MAPE reduced to 1.45 and 3.40%, respectively. In the proposed model, when the time lags were set to three, the MAE and MAPE were 1.17 and 2.73, but as the number of time lags increased from three onward, the performance behavior of the proposed model was not decreased as it was in the baseline models. The proposed model achieved its best performance when time lag was set as three, the MAE and MAPE reduced to 1.17 and 2.73%, respectively. As the number of time lags increased from three onward, the performance of the proposed model did not decrease as did the baseline models. The experimental results are shown in Tables 2 and 3. Figure 7 shows the comparison of different models' training times per epoch. The graphical representation of the results are shown in Figures 8 and 9. The ground truth speed values and predicted speed values of the proposed model at the sensor station 167.56 milepost, from a randomly selected day, while predicting multistep future traffic speed prediction on 15, 30, and 60 min time frames are shown in Figure 10. We used the same sensor location to clearly show the performance of the proposed model with different time steps without having biased or ambiguous results. \begin{table}
\begin{tabular}{l l} \hline Time lags & 3, 6, and 12, respectively \\ Total time steps & 105,120 \\ Activation function & Sigmoid \\ Training process & Mini-batch gradient descent \\ Optimizer & RMSProp \\ Loss & MSE \\ Patience & 20 \\ Training sample & 75,679 \\ Validation samples & 18,920 \\ Number of trainable parameters & 3,491,173 \\ Number of nontrainable parameters & 256 \\ Total parameters & 3,491,429 \\ \hline \end{tabular}
\end{table} 
Table 1: Hyperparameters. Figure 8: MAE vs. time lags. Figure 7: Training time per epoch vs. time (seconds). Figure 9: MAPE vs. time lags.