## 2 Literature Review
### Identified Gaps and Research Justification  
International scholarship on waiting times is dominated by mega-cities whose services run in exclusive rights-of-way or benefit from tight real-time control. Examples include London, where segregated bus lanes and dynamic headway management shape empirical work on stop-level delay distributions by [PERSON] et al. [29], and TfL's studies of perceived versus actual wait costs [30]; Seoul, where smart-card big-data analytics have served to improve bus scheduling models and optimize service intervals based on actual passenger demand by [PERSON] and [PERSON] [31]; and Beijing, where field observations and video recordings characterize waiting passenger distributions in a fully grade-separated subway environment by [PERSON] et al. [32].  
By contrast, Greater Valparaiso features a complex topography--steep hills forming a natural amphitheater-like setting--and a historic hillside core, inscribed on UNESCO's World Heritage List in 2003 [33] and examined in depth by [PERSON] and [PERSON] [34]. Moreover, while over thirty funicular elevators were built during the 19 th and 20 th centuries to connect the hills with the flat areas, fewer than half remained operational at the turn of the 21 st century, and several are now undergoing restoration by [PERSON], [PERSON] and [PERSON] [35]. These traits generate irregular headways and highly localized delays that international models do not capture.  
In addition, the 2014 Gran Valparaiso Mobility and Transport Survey remains the only publicly accessible micro-level dataset providing georeferenced origin-destination trip records alongside detailed socio-demographic attributes (see Section 3.1 \"Database Description and Preprocessing\"). The implications of its ten-year age are discussed in the Outdated Database subsection (Section 5.1), where official SECTRA and municipal reports for 2020-2024 indicate only minor changes in network layout and vehicle operation--validating the 2014 data as a reliable historical baseline for our spatial analysis.  
Methodologically, while some equity analyses rely on regional averages, others apply spatial statistics like local Moran's I to transit accessibility metrics to control for spatial autocorrelation and reveal local clusters ([PERSON] and [PERSON] [6]), while data-driven passenger segmentation relies on DBSCAN variants but omits spatial autocorrelation ([PERSON] et al. [36]). Fast implementations of DBSCAN now leverage randomized kd-forest and priority-search k-means tree acceleration for approximate neighbor queries, as shown by [PERSON] and [PERSON] [37], yet none have been applied to public transport waiting time analysis. In Valparaiso, recent work examines metro ridership-built-environment interactions ([PERSON] et al. [38]), whereas analyses of hillside mobility constraints in steep terrain characterize sustainable mobility patterns but do not address temporal reliability ([PERSON] and [PERSON] [34]).  
Consequently, gaps persist regarding (i) how Valparaiso's unique mix of modes and topography modifies waiting time patterns; (ii) how spatial dependence interacts with user heterogeneity at a sub-municipal scale; and (iii) whether advanced clustering can reveal vulnerable groups invisible to aggregate metrics.  
Our study addresses those gaps by combining local survey micro-data with an integrated workflow--exploratory analysis, global Moran's I, and a kd-tree-optimized, expansion-factor-weighted DBSCAN--to map clusters of excessive waits and link them to socio-demographic profiles. The results inform frequency planning and equity-oriented policy for cities that share Valparaiso's steep terrain and mixed heritage fleets.