# Travel Time Prediction on Long-Distance Road Segments in Thailand
## 4. Results and Discussions
### Discussion  
The aim of our work was to improve the accuracy of a travel time prediction model using a time-series technique. Our dataset was the GPS transactions of trucks in Thailand, as depicted in Figure 3. A closer look at the data indicated that the location of trucks with a timestamp could be viewed as time-series data. Thus, we sampled the raw data according to the average hourly travel times of 10 road segments of a long distance, as presented in Table 1. To create an approach for the generation of a travel time prediction model, several time-series forecasting techniques were studied from related works. (1) In the first experiment, we attempted to find a suitable time-series technique for our baseline. The result of the experiment was that the LSTM provided the best performance. The results from Table 3 were interpreted as follows: the LSTM model provided an error of \(\pm\)27.12 min in every 100 km. This error range, being almost half an hour, was regarded as being too high in error. Thus, in this case, this issue became the main focus of our study, and it was our challenge to solve this problem. (2) In the second experiment, the LSTM was improved with the addition of self-attention, becoming an SA-LSTM. The results presented in Table 4 show that the SA-LSTM was better than the LSTM. Although the MAE was slightly reduced, \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Road Segment**} & **Distance** & \multicolumn{2}{c}{**MAE (minutes) per 100 km**} & \multirow{2}{*}{**\%**} \\  & **(km)** & & **Baseline** & **Our Approach** & **Improvement** \\ \hline Highway No. 1 & 332 & 9.19 & 4.04 & 56.08\% \\ Highway No. 2 & 232 & 22.06 & 9.15 & 58.53\% \\ Highway No. 4 & 219 & 13.70 & 6.01 & 56.15\% \\ Highway No. 7 & 95 & 49.66 & 25.41 & 48.83\% \\ Highway No. 9 & 149 & 29.89 & 12.88 & 56.92\% \\ Highway No. 32 & 143 & 31.65 & 14.29 & 54.86\% \\ Highway No. 35 & 75 & 17.35 & 8.23 & 52.57\% \\ Highway No. 41 & 242 & 14.16 & 6.36 & 55.11\% \\ Highway No. 304 & 104 & 19.47 & 8.16 & 58.07\% \\ Highway No. 331 & 80 & 64.03 & 26.98 & 57.87\% \\ \hline
**Average** & & **27.12** & **12.15** & **55.20\%** \\ \hline
**Standard Deviation** & & & & \\
**(STD)** & & **17.47** & **8.01** & **0.03** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: A comparison of the baseline and our approach for all road segments. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Techniques**} & \multicolumn{2}{c}{**Computation Time (Seconds)**} \\ \cline{2-3}  & **Training** & **Predicting** \\ \hline ARIMA & 146.56 & 0.04 \\ SVR & 8.16 & 0.55 \\ ConvLSTM & 493.86 & 1.25 \\ LSTM (only) & 337.08 & 0.58 \\ SA-LSTM & 320.14 & 0.58 \\ SA-LSTM + Kalman filter & 327.13 & 0.58 \\ SA-LSTM + Savitzky-Golay filter & 331.26 & 0.58 \\ SA-LSTM + Butterworth low-pass filter & 314.61 & 0.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Computation times of each technique in our experiment. this was a sign of enhancement of the model. (3) In the last experiment, we tried to find an appropriate filter method for data cleansing. The results in Table 5, using the Butterworth low-pass filter with SA-LSTM, were the best among all the experiments. This may have been due to the noise of the original data having a high impact on the performance of the prediction model. When this filter was applied, the MAE of the SA-LSTM was reduced from 26.89 to 12.15. Based on the experimental results, our best approach was to use the SA-LSTM model with the Butterworth low-pass filter. As we analyzed for each road, as shown in Table 6, we can conclude that the improvement of most road segments was greater than 50%, and the total improvement was 55.20%. Although the MAEs of all the road segments had high variance, as indicated by the standard deviation (STD) in the table, the percent improvements of all the road segments were not much different. This means that our method achieved a relatively stable improvement rate.