## 5 Conclusions  
In this study, a DNN was used to develop a highway crash prediction and warning model. A data association framework was used to create datasets comprising large volumes of ETC and VD data, which included information on shock wave propagation, mean traffic speed, and headway defined by traffic flow theories. To obtain training data for the proposed model, the associations between these data and gantry information, accident location, and accident quantity were examined. Generally, the adopted framework can be used to establish the relationships between actual sensor data (e.g., mean traffic speed, lane occupancy rate, and traffic flow volume) and traffic accident occurrences. For example, when the traffic density is uneven, shock waves are generated, which in turn affect changes in the mean traffic speed of vehicles. Therefore, to identify the occurrence of traffic accidents, drastic decreases in vehicle headway and mean traffic speed recorded in datasets must be examined. In this study, sensor data and traffic flow theories were combined to label all data entries as either accident or no-accident instances in order to create datasets for testing and validating the developed DNN model. The class weight method was used to address the problem of imbalanced data, thereby allowing the proposed model to accurately predict traffic accidents. The test results indicated that the proposed model exhibited high accuracy and sensitivity and a low false alarm rate. Specifically, the model accurately predicted 88% of traffic accidents while generating a false alarm rate of 6% and 5% during the training and validation stages, respectively. Overall, the model exhibited an accuracy of 94%. However, only the data recorded at gantry 01F1960S and its neighboring upstream and downstream gantries (01F1906S and 01F2011S, respectively) were examined. Therefore, future studies should focus on all lanes and sections of highways to develop a model that produces different prediction results depending on regional characteristics, thereby increasing the flexibility of the model construction method proposed in this study. In conclusion, the data association framework and prediction model proposed in this study have high potential for smart highway management aiming to improve the safety of road users. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**(a)** Training dataset} \\ \hline \multicolumn{4}{c}{**Total Number of Data: 84,048**} \\ \hline \multicolumn{4}{c}{**Model Prediction**} \\ \cline{2-4}
**Classification** & \multicolumn{2}{c}{**Accident Occurs**} & **No Accident** \\ \hline \multirow{2}{*}{Actual situation} & Accident occurs & 499 (TP) & 68 (FN) \\  & No accident & 4725 (FP) & 78,576 (TN) \\ \hline \multirow{2}{*}{Sensitivity: Precision:} & 88\% & False alarm rates: & 6\% \\  & 10\% & Accuracy: & 94\% \\ \hline \multicolumn{4}{c}{**(b)** Testing dataset} \\ \hline \multicolumn{4}{c}{**Total Number of Data: 21,071**} \\ \hline \multicolumn{4}{c}{**Classification**} & \multicolumn{2}{c}{**Model Prediction**} \\ \cline{2-4}  & \multicolumn{2}{c}{**Accident Occurs**} & **No Accident** \\ \hline \multirow{2}{*}{Actual situation} & Accident occurs & 119 (TP) & 17 (FN) \\  & No accident & 1144 (FP) & 19,791 (TN) \\ \hline \multirow{2}{*}{Sensitivity: Precision:} & 88\% & False alarm rates: & 5\% \\  & 9\% & Accuracy: & 94\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Confusion matrix and performance indicators of the proposed prediction model. **Author Contributions:** [PERSON] and [PERSON] proposed the conceptual idea of this study. [PERSON] and [PERSON] carried out the data survey and data collection. [PERSON] and [PERSON] carried out methodology development and overall architecture design. Finally, the writing--review and editing was done by [PERSON]. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding.