## 5 Conclusions  
In this study, we propose a method to predict bus arrival times in the Gangnam area by applying linear projection, learnable location-encoding techniques, and a fully connected layer within a transformer-encoder model. The approach is compared with time series forecasting models GRU, LSTM, Bi-LSTM, transformer-encoder model, and fully connected neural network (FCNN) model. The proposed BAT-Transformer model performed well in predicting bus arrival times by effectively learning the temporal characteristics of the data using these techniques. The performance-evaluation results showed that the BAT-Transformer model achieved a low RMSE of 92 and a relatively low MAPE of 35%. This means that the BAT-Transformer model fits the training data well and achieves higher prediction accuracy than the traditional BIS error time, which indicates that the transformer model fits the training data well and achieves high prediction accuracy. In addition, the BAT-Transformer model converged faster and had lower loss and RMSE values than other models, suggesting that it effectively handles complex time series data and learns various patterns to achieve high prediction accuracy. These results demonstrate the superiority of the model and highlight its stability and consistency even on large datasets, enhancing its applicability in real-world scenarios. Furthermore, the BAT-Transformer model outperforms the other models in terms of MAPE and TWE, indicating better prediction accuracy and reduced prediction error on real data. However, in terms of the R\({}^{2}\) metric, the FCNN model records higher values, suggesting a better explanation of data variability. This indicates that the BAT-Transformer model may be somewhat deficient in fitting the data. Nevertheless, this study shows the superior performance of the BAT-Transformer model by prioritizing prediction accuracy and error reduction. Future research should focus on improving data fitting to address this aspect. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Loss** & **RMSE** & **MAPE** & **R\({}^{2}\)** & **TWE** \\ \hline GRU & 31,921 & 204 & 69 & 0.58 & 137 \\ \hline LSTM & 20,170 & 153 & 57 & 0.55 & 107 \\ \hline Bi-LSTM & 15,651 & 125 & 54 & 0.7 & 96 \\ \hline FCNN & 20,170 & 142 & 53 & 0.94 & 97 \\ \hline Transformer Encoder & 15,123 & 122.6 & 51 & 0.76 & 93 \\ \hline
**BAT-Transformer** & 8722 & 92 & 35 & 0.83 & 66 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparisons of BAT-Transformer and others. The main objectives of this study were to experimentally demonstrate that the linear projection process, learnable location-encoding technique, and fully connected layer applied to the transformer-encoder model outperform other models in predicting bus arrival-prediction error time. We also verified that the data-resampling technique can effectively handle unbalanced datasets and improve the learning performance of the model, and systematically evaluated the performance of the model using various metrics to verify its practical applicability. However, there are some limitations to this study. Additional data-collection and -preprocessing is needed to achieve more consistent performance improvements, lighter model designs should be considered, and optimization techniques should be explored to reduce the complexity and computational cost of the converter model. These aspects will be addressed in future work. In future work, experiments will be conducted in different environments to validate the generalization capabilities of the transducer model and explore its potential as a real-time prediction system. This study demonstrates the feasibility of using transducer models for bus arrival time prediction, which may contribute to improving the efficiency of public transportation systems in the future. Conceptualization, [PERSON]; methodology, [PERSON]; software, S.J. ; validation, S.J. ; formal analysis, S.J. ; investigation, S.J. ; resources, S.J. ; data curation, S.J. ; writing--original draft preparation, S.J.