# A Cox Model-Based Workflow for Increased Accuracy in Activity-Travel Patterns Generation
## 4 Results
### ABM's Outputs and Traffic Analysis Results  
One of the features of the open-source ABM that is used as part of this research work is Traffic Analysis based on the synthetic data generated. This analysis, and the respective data that can be collected, as they are plotted in Figures 4-8 of the current section and Figures 10 and 11 in Appendix A, can serve as an interesting input to any transport planning process. Figures 4 and 5 focus on the hourly distribution of trips by income group, before and after the intervention, respectively. While the overall structure of trip activity remains consistent, subtle yet significant shifts are observable, particularly among lower-income groups, which exhibit a redistribution of trip frequencies toward the midday period post-intervention. This suggests a refinement in activity duration estimates, which better aligns synthetic behavior with known empirical patterns. In contrast, higher-income groups maintain a more bimodal distribution centered around conventional commuting hours, but with slightly sharper peaks after the intervention, indicative of improved modeling of work-related trip timings. Figure 6 further reinforces this finding by juxtaposing the aggregate hourly trip percentages across the two scenarios (pre- and post-intervention). The inclusion of Cox-based duration estimation yields a smoother and more realistic temporal curve, especially during \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metrics** & **Synth. Data 1** & **Synth. Data 2** & **Synth. Data 3** & **Synth. Data 4** \\ \hline K–S test & 0.25078/ & 0.2253/ & 0.18736/ & 0.24032/ \\ (D/\(p\)-value) & 0.000972 & 0.02735 & 0.1031 & 0.01534 \\ \hline MAE & 4.047721 & 3.91789 & 3.951568 & 3.971024 \\ \hline RMSE & 5.132352 & 5.062376 & 5.040041 & 4.999081 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of real vs. synthetic data for education purposes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metrics** & **Synth. Data 1** & **Synth. Data 2** & **Synth. Data 3** & **Synth. Data 4** \\ \hline K–S test & 0.47753/ & 0.2801/ & 0.35482/ & 0.31586/ \\ (D/\(p\)-value) & 8.42 \(\times\) 10\({}^{-8}\) & 0.005868 & 0.0001707 & 0.001193 \\ \hline MAE & 4.755 & 4.5188 & 4.3898 & 4.45858 \\ \hline RMSE & 6.1339 & 5.9359 & 5.8461 & 5.921535 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparison of real vs. synthetic data for other purposes. late afternoon and evening periods, where unprocessed data previously underrepresented trip volume. These refinements support the hypothesis that data-driven duration correction enhances the fidelity of synthetic activity chains. In spatial terms, Figures 7 and 8 depict traffic density distributions before and after the intervention, focusing on market-related and car-mode trips, respectively. The maps use a color gradient, from light blue for lower densities to magenta for higher densities, to  
Figure 4: Percentage of Trips by Hour and by Income group _before_ the intervention proposed in this research. Figure 5: Percentage of Trips by Hour and by Income group _after_ the intervention proposed in this research. Figure 6: Hourly comparison of the percentage of trips for the scenarios when the workflow does not include the Cox-based models for activity duration estimation (purple), and when it includes (orange). highlight variations across both time and space. Notably, post-intervention distributions show broader and more nuanced traffic dispersal, particularly in peripheral zones, indicating a better representation of non-central urban activity. This suggests that the intervention enables the ABM to capture not only core commuting behaviors but also discretionary and decentralized trip patterns more effectively. Figures A1 and A2, included in Appendix A, present cumulative frequency plots of trips per age group generated by the ABM using the original and enhanced workflows, respectively.