# Travel Time Prediction on Long-Distance Road Segments in Thailand
## 4. Results and Discussions
### Discussion
This result can also be visualized in the line chart in Figure 8. It shows values of actual travel time points (solid black line) and the predicted values (red dashed line) of a few days from all selected road segments. In addition, our approach specifically emphasized the GPS data and viewed the GPS transactions as time-series data. The road data were also used to support the selection of road segments that had a high occurrence of vehicles passing through them. Thus, to work with our approach, we recommend that machine-learning developers collect GPS transactions of vehicles, including vehicle identifiers, latitude, longitude, and timestamps. It should be noted that the road data were further used to find reference points to identify  
Figure 8: Line chart visualizing the comparison between actual values (black solid line) and predicted values (red dashed line) using the SA-LSTM model with Butterworth low-pass filter from each road segment of a few days. road sections. Then, both datasets were analyzed into time series of travel time of each selected road segment, and this dataset was used as the input for our method. As reviewed in the related studies in Section 2, several works, including the LSTM model discussed by [PERSON] et al. [13], the LSTM model of [PERSON] et al. [20], and the ConvLSTM model of [PERSON] et al. [14], inspired our work. First, the model of [13] is closest to our work in terms of an LSTM with attention. It used interval data of 15 min as data points and used seven data points as an input of the LSTM and forwarded these to the attention layer to predict the travel time of the following data point. For our approach, we used the LSTM with self-attention and considered 24 input units at one-hour intervals. The experiments from [13] and our work also show that using the LSTM with attention is better than that without attention; the experiment results from [13] showed a 3.19% improvement, while our work had an improvement of 0.84%. Although this improvement is somewhat low, using attention can be a good means of increasing the performance of the LSTM model. Second, the model of [20] considered an LSTM without attention. It also used interval data as the input data in order to predict the subsequent data points. For the long-term prediction, the goal was to use 182 days to predict the travel time of the following 30 days. In our work, we attempted to use the travel time of the previous 24 h to predict the travel time of the following hour. Finally, the ConvLSTM model from [14] used the convolutional layers after LSTM. Although the ConvLSTM did not give a good result in our experiment, it evidenced that the use of self-attention can slightly improve the model. This work also stated that the LSTM played a key role when near-term data were highly correlated to the subsequent travel time. In addition to the selected studies [13; 14; 20], our model considered the selection of a filter method, which was the Butterworth low-pass filter, to process the input data. This filter method is generally applied in time-series analytics [23; 24]; however, it might not be necessary for the three selected studies. As we learned from the related studies and our approach, the architecture of the travel time prediction model can be customized. In the case of using the LSTM as a core technique, the hyperparameters, such as the number of LSTM units, must be adjusted. In addition, other assembly techniques, such as attention layers, convolutional layers, and filter methods, should be considered. This consideration is based on an experimental environment, including datasets, goals, and evaluation methods. According to our dataset and the results of the experiments, our travel time prediction model became a Self-Attention LSTM with a Butterworth low-pass filter that can process the travel time of the previous 24 h to estimate that of the following hour. Since this study was strongly focused on the GPS data, the historical travel time data were a key factor in the prediction of future travel time.