## 4 Application
### Dataset Adequacy and Validation  
Given the complexity and the number of indices introduced in UTMOM, ensuring that our dataset is sufficient for robust modeling is crucial. To address potential concerns about the dataset size, we have implemented several strategies to confirm its adequacy:  
* Dataset Augmentation and Preprocessing: We applied various data augmentation techniques to enhance the dataset, ensuring it captures a wide range of traffic scenarios. This includes synthetic data generation for underrepresented traffic conditions, thereby increasing the diversity and volume of the training data. * Cross-Validation: To maximize the use of available data for training and validation, we employed cross-validation techniques. This approach tests the model on multiple subsets of the data, enhancing its generalizability and robustness. * Empirical Analysis: An empirical analysis was conducted to determine the minimum dataset size required for reliable modeling. This analysis took into account the complexity of the indices and the variability in traffic patterns. The results confirmed that the current dataset meets these requirements. * Incremental Training: We implemented incremental training methods, where the model is trained on smaller subsets of data progressively. This approach allows for continuous learning and validation as more data become available, ensuring that the model remains up-to-date and accurate. * Statistical Validation: We performed statistical tests to validate the sufficiency of the dataset size. These tests ensured that the training and validation sets are representative of broader traffic patterns, thereby enhancing the reliability of the model's predictions. By employing these strategies, we ensured that our dataset is adequate for the complexity of the model and that the findings are both reliable and applicable. These measures \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Day** & **Moring (Dataset 1)** & **Morming (Dataset 2)** & **Afternoon (Dataset 1)** & **Afternoon (Dataset 2)** & **Evening (Dataset 1)** & **Evening (Dataset 2)** \\ \hline
1 & 180 & 231 & 287 & 356 & 951 & 1172 \\
2 & 231 & 252 & 279 & 391 & 1029 & 1169 \\
3 & 231 & 354 & 320 & 315 & 998 & 1194 \\
4 & 203 & 219 & 276 & 347 & 967 & 1165 \\
5 & 188 & 198 & 172 & 359 & 852 & 1225 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Observed Traffic Data Summary. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Day** & **Min\_Vehicle\_Count** & **Max\_Vehicle\_Count** & **Max\_Change** & **Max\_Inconsistency** & **Actual\_Totals (Dataset 1)** & **Actual\_Totals (Dataset 2)** \\ \hline
1 & 172 & 1225 & 23 & 54 & 7163 & 8947 \\
2 & 172 & 1225 & 23 & 54 & 7163 & 8947 \\
3 & 172 & 1225 & 23 & 54 & 7163 & 8947 \\
4 & 172 & 1225 & 23 & 54 & 7163 & 8947 \\
5 & 172 & 1225 & 23 & 54 & 7163 & 8947 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Model Constraints and Parameters Summary. are detailed to provide a clear understanding of our data validation process, confirming that the dataset size is sufficient for the robust modeling required by UTMOM. To ensure robust validation of UTMOM, we separated the dataset into distinct parts for training and validation:  
* Training Set: Comprising approximately 70% of the total dataset, this portion was used to train UTMOM, ensuring sufficient data to learn patterns and relationships within the traffic data. * Validation Set: The remaining 30% of the data was reserved for validation purposes, providing an unbiased evaluation of the model's predictive capabilities on unseen data. Additionally, we employed k-fold cross-validation to further ensure the robustness of our model. This method involves partitioning the training data into k equally sized folds. The model is trained on k \(-\) 1 folds and validated on the remaining fold, with the process repeated k times. The results are then averaged to provide a comprehensive assessment of the model's performance.