## 4 Results and Discussion
### Clustering Analysis (DBSCAN) and Discussion
Cluster with Waiting Times Near the Average. Cluster 0 is the largest group, encompassing users with waiting times close to the overall average. Most of these users are students who use urban buses in the Santa Julia macrozone to return home. Although the waiting times are not exceedingly long, there is some variability, indicating opportunities to enhance service regularity. 3. Clusters with High Waiting Times. These clusters are of particular interest because users experience waiting times significantly above the average, negatively affecting their experience and satisfaction with public transport. According to the definition provided in Section 3.2.3, clusters with mean waiting times \(\geq\) 20 min and above the global average of 7.20 min (i.e., clusters 3, 4, 6, and 8) are classified as'most affected users'. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Cluster** & **Size** & **Avg. Waiting** & **Std. Dev.** & **Most Common** & **Most Common** & **Most Common** & **Most Common** \\  & & **Time (min)** & **(min)** & **Transport Mode** & **Occupation** & **Home** & **Macrozone** & **Trip Purpose** \\ \hline
0 & 13 & 6.92 & 5.19 & Urban Bus & Student & Santa Julia & Returning Home \\
1 & 3 & 5.77 & 4.47 & Taxi Colectivo & Employee or & Valparaiso Alto & Returning Home \\
2 & 822 & 5.90 & 3.20 & Metro Valparaiso & Employee or & Villa Alemana & Returning Home \\
3 & 34 & 39.88 & 0.48 & Urban Bus & Employee or & Santa Julia & Returning Home \\
4 & 20 & 34.95 & 0.22 & Urban Bus & Unpaid Family & Viña del Mar & Returning Home \\  & & & & & & \\
5 & 68 & 4.16 & 1.85 & Trolleybus & Employee or & Valparaiso Alto & Returning Home \\
6 & 38 & 30.00 & 0.00 & Taxi Colectivo & Employee or & Forestal & Returning Home \\
7 & 37 & 3.14 & 1.57 & Funicular & Employee or & Valparaiso Alto & Returning Home \\  & & & & & & \\
8 & 8 & 60.00 & 0.00 & Urban Bus & Employee or & Miraflores & Returning Home \\ \(-1\) (Noise) & 154 & N/A & N/A & N/A & N/A & N/A & N/A \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Characterization of the identified clusters. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Clusters with Low Waiting Times (Below** & **Clusters with Waiting Times Near** & **Clusters with High Waiting Times** \\  & **the Overall Average of 7.20 Minutes)** & **the Average** & **(Significantly Above the Average)** \\ \hline Cluster 5: 4.16 min & Cluster 0: 6.92 min & Cluster 3: 39.88 min \\ Cluster 7: 3.14 min & Cluster 4: 34.95 min \\ Cluster 1: 5.77 min & Cluster 6: 30.00 min \\ Cluster 2: 5.90 min & Cluster 8: 60.00 min \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Waiting time clusters. Cluster 3: Users predominantly from Santa Julia using urban buses, with an average waiting time of 39.88 min. Moreover, the low standard deviation indicates that all users in this cluster experience similar waiting times, pointing to a systemic frequency or availability issue in urban bus service in Santa Julia. As shown in Figure 6, most trips start or end in a peripheral area. Cluster 4: Users primarily from Vina del Mar Oriente, also relying on urban buses, with an average waiting time of 34.95 min. Though this is a small cluster, it highlights a critical situation where vulnerable users, such as unpaid family members, face lengthy waits, potentially affecting their access to services and opportunities. The spatial distribution of trips in this cluster is shown in Figure 7.  
Figure 6: Satellite view of origin–destination trips for cluster 3. Figure 7: Satellite view of origin–destination trips for cluster 4. Cluster 6: Users primarily from Forestal who use Taxi Colevtivos, with a fixed waiting time of 30.00 min. The absence of variability and the fixed wait time suggest specific schedules or limited Taxi Colevtivo availability in Forestal, negatively impacting residents' mobility. The spatial distribution of trips in this cluster is shown in Figure 8.  
Cluster 8: Users primarily from Miraflores who use urban buses, encountering a maximum waiting time of 60.00 min.