Equity-based spatial clustering of unmet DRT demand for fixed-route transit optimization in underserved areas

Introduction

Over the past decade, urban transportation has undergone a significant transformation (Zou et al., 2025; Brownrigg-Gleeson et al., 2025), driven by advances in digital technologies (Lei et al., 2025; Khaleel et al., 2025; Mahgoub, 2025), the growing need for environmental sustainability, and the increasing demand for more equitable and efficient mobility services (Delponte and Costa, 2022). One of the innovative approaches reshaping public transit is Demand-Responsive Transit (DRT). This flexible, user-focused transportation mode adjusts routes (Grau et al., 2025; Turno and Yatskiv, 2023) and schedules in real time (Yeon et al., 2025; Fielbaum et al., 2021) or based on pre-booked passenger demand. Unlike conventional Fixed-Route Transit (FRT) systems, which operate along static routes with predetermined stops, DRT systems offer on-demand mobility that better serves sparsely populated or underserved areas (Kaufman, 2022; Hosseini et al., 2025; Gökay, 2021; Charlton, 2024; Shahin et al., 2024).

The potential of DRT to complement and expand the reach of traditional transit systems is significant in mid-sized cities like Kalamazoo, Michigan, where a combination of dense urban centers and low-density neighborhoods creates challenges for providing consistent and fair transit access. In many such areas, conventional bus routes are either too costly or too inefficient to operate, leaving large parts of the population without adequate mobility choices (Baier et al., 2024; Humann, 2024). These include vulnerable groups such as low-income residents, elderly individuals, people with disabilities, and those without private vehicles. Therefore, DRT offers a promising solution to address these accessibility gaps by providing demand-driven, context-aware transportation options.

Despite its promise, DRT has often been implemented in isolation, disconnected from the broader transit ecosystem. This fragmentation limits its effectiveness and often fails to meet users’ expectations for reliability, accessibility, and convenience. Integrating DRT with FRT into a hybrid transit model could substantially improve system-wide efficiency and enhance user experience, particularly when guided by spatiotemporal demand data and optimization algorithms. However, such integration remains underexplored in both academic literature and real-world planning efforts.

This study addresses the gap by proposing a comprehensive framework for spatiotemporal simulation of hybrid transit systems, with a specific focus on integrating DRT with FRT in the Kalamazoo region. Using data from multiple sources, including General Transit Feed Specification (GTFS), demographic and socioeconomic datasets, and transit service logs, this research aims to identify mobility patterns, underserved areas, and optimal opportunities for DRT intervention. The study employs advanced analytical techniques, including survival analysis, agent-based modeling, spatiotemporal clustering, and machine-learning-based forecasting, to evaluate and simulate transit operations across space and time.

Literature review

The growing interest in Demand Responsive Transit (DRT) has led to a substantial body of research investigating its operational efficiency, user equity, spatial and temporal performance, and potential integration with conventional transit systems. Studies have highlighted the transformative potential of DRT in both urban and rural contexts, particularly in areas with sparse transit coverage or unique socio-demographic needs.

Sanaullah et al. (2021) conducted a spatio-temporal study of DRT in Belleville, Canada, using real-time operational data. They revealed that ridership is strongly influenced by land use and time-of-day patterns, reinforcing the value of DRT in complementing fixed-route services, particularly during off-peak hours. Similarly, Huo et al. (2021) utilized multi-source datasets to uncover that DRT ridership is significantly correlated with employment density and proximity to traditional transit stops. These studies underscore the spatial sensitivity of DRT demand and its potential to support service equity in underserved areas.

Addressing equity more directly, Son and Kim (2022) applied survival analysis to examine waiting times for people with disabilities in Seoul. They found spatial and temporal disparities, calling for more inclusive DRT deployment strategies. Sadraddini (2023) took a related approach in Toronto, recommending spatiotemporal segmentation to improve paratransit accessibility for vulnerable users. In another study focused on accessibility, Nakajima and Kato (2025) examined a DRT pilot in Senboku, Japan. Using a cohort design with propensity score matching, they found that DRT participation increased average daily walking steps and improved health-related quality of life.

In terms of DRT planning and demand prediction, recent literature has emphasized data-driven and adaptive approaches. Melo et al. (2024) proposed integrating mobile data analytics into DRT route planning to identify real-time demand patterns that improve service responsiveness. Wang et al. (2023) focused on pricing strategies and proposed discount-based aggregation mechanisms that encourage ride-sharing while increasing profitability. Al-Nabulsi et al. (2025a) introduced an advanced graph-based deep learning framework that integrates Graph Convolutional Networks with a Deep Multi-View Spatial-Temporal Network to forecast DRT demand. Meanwhile, Lee et al. (2024) tackled the issue of sparse demand by developing a deep learning model that accurately predicts DRT usage based on both probability and volume.

Several studies have also examined DRT implementation in rural and low-density contexts. Martí et al. (2023) highlighted infrastructure and technological gaps that limit DRT expansion in rural regions, while Huang (2025), using the RECAP framework, developed a classification matrix to match DRT models to local territorial characteristics. In Switzerland, Imhof and Blättler (2023) applied machine learning to trip data from the rural mybuxi service and found that population density, distance to train stations, and the presence of amenities were key predictors of DRT usage more so than conventional public transport quality indicators. Al-Nabulsi et al. (2025b) developed a dual-model framework that integrates real-time simulation with CVRPTW optimization to quantify trade-offs between fleet efficiency and passenger delay in DRT systems, demonstrating the operational sensitivity of service rates, delay thresholds, and vehicle allocation strategies.

Socio-demographic analyses have also featured prominently. Kaufman et al. (2021), analyzing the Logan DRT trial in Australia, reported that most users lacked access to private vehicles and relied heavily on DRT to access essential services. Similarly, Yang and Cherry (2017) studied DRT use in rural Tennessee and found that users were primarily lower income “captive riders” dependent on DRT for medical needs. Jevinger and Svensson (2024) further revealed that age-specific preferences influence DRT acceptability, with older adults less receptive to digital interfaces and more concerned with comfort and reliability.

A significant operational contribution was made by Liang et al. (2025), who developed a super spatiotemporal network model to integrate hybrid fleet management for DRT, providing insights into scheduling and energy use in mixed-fuel electric transit systems. Kim et al. (2025) also made methodological contributions by applying spatial causal inference to assess DRT’s impact on transit equity, confirming improvements in accessibility in marginalized areas.

Additional research from Park and Jung (2019) and Pasaribu (2023) explored the replacement of traditional bus services with DRT in Korea and Norway, respectively. Park and Jung identified factors influencing resistance to DRT adoption in low-demand areas. At the same time, Pasaribu evaluated cost-effective DRT schemes and developed predictive logit models using mobility and demographic data. In Italy, D’Orso et al. (2025) conducted a DRT pilot in Palermo and confirmed reductions in waiting and travel times, although financial feasibility remained a concern.

Wang et al. (2014) employed multilevel modeling to investigate the socio-economic influences on DRT demand in Greater Manchester. Their results showed that lower car ownership, higher deprivation, and low-density neighborhoods are key drivers of DRT usage, emphasizing the system’s relevance to socially vulnerable groups.

To support synthesis and comparison, Table 1 serves as a comparative reference highlighting the diversity of approaches—ranging from machine learning and deep learning models to cohort studies, survival analysis, and multilevel regression—and geographic coverage spanning North America, Europe, and Asia.

TABLE 1. Spatiotemporal Strategies case studies.

Despite the growing body of literature on Demand-Responsive Transit (DRT), relatively limited prior work has systematically integrated spatial demand diagnostics with equity-based prioritization to proactively guide service deployment. Most studies evaluate DRT performance post-implementation, focusing on operational efficiency, ridership behavior, or cost impacts. Fewer studies provide a spatially explicit, pre-deployment framework that identifies micro-level demand concentrations and aligns them with socio-demographic vulnerability indicators. As a result, practical tools for diagnosing and ranking underserved areas in hybrid fixed-route–DRT systems remain comparatively underdeveloped.

This research addresses that gap by developing a replicable spatial prioritization framework that blends actual trip origin-destination data with fixed-route transit locations, equity indicators, and clustering techniques. Using geospatial buffer analysis and DBSCAN clustering, it identifies demand hotspots that fall outside accessible fixed-route coverage. It then introduces a novel “priority score” that ranks clusters based not only on trip volume but also on socio-demographic need, such as poverty levels, disability rates, and median income. This approach ensures that areas selected for DRT intervention are not only operationally justified but also socially impactful. The final output provides planners with clear, time-specific, and zone-based recommendations, transforming a diagnostic exercise into a practical roadmap for expanding equitable DRT services.

Methodology

To evaluate spatial and equity-based gaps in public transportation coverage in Kalamazoo, Michigan, a four-phase analytical framework was developed in Figure 1. The framework integrates spatial diagnostics, density-based clustering, and equity-oriented modeling to support data-driven prioritization and route planning for Demand-Responsive Transit (DRT) services. Kalamazoo’s transit system is primarily composed of fixed-route services operated by Metro Transit, which effectively serve the urban core but leave peripheral neighborhoods and low-density areas underserved. To capture realized mobility demand beyond the reach of fixed-route infrastructure, 1 month (October 2019) of real-world DRT trip data from a flexible mobility pilot was analyzed. The dataset includes geocoded pick-up and drop-off locations with timestamps, enabling a detailed spatial assessment of unmet demand patterns. Fixed-route coverage was represented using General Transit Feed Specification (GTFS) data from 2024, while socio-demographic indicators, including income, poverty status, disability prevalence, and vehicle ownership, were derived from the American Community Survey (ACS) 5-year estimates (2019–2023). All datasets were spatially harmonized to ensure consistency across the multi-phase analysis.

The initial phase concentrated on pinpointing geographic areas where fixed-route service does not meet actual demand. This involved mapping all DRT trip origins and destinations and overlaying them with bus stop locations obtained from General Transit Feed Specification (GTFS) data. A buffer and sensitivity analysis were performed using various radii (from 0.1 to 0.5 miles) around each fixed route stop to define the effective service area. Incorporating GTFS enabled a spatially detailed identification of “transit desert” areas, which are entirely lacking fixed-route access, highlighting the structural constraints of the existing network.

To delineate the spatial extent of existing transit coverage, geospatial buffers were generated around all fixed-route bus stops in Kalamazoo. Let:

β = b 1 , … . , b M ⊂ R 2 : Coordinates of fixed routes bus stop

T = o i , d i i = 1 N : Set of DRT trips with origin O i and destinatin d i

r ∈ R + : B uffer raduis used to construct service areas

. 2 : Euclidean norm

For each stop b j, define the closed buffer zone.

S r b j = x ∈ R 2 : x − b j 2 ≤ r

The total serviceable area at radius r is the union of all buffer zones

A r = ⋃ j = 1 M S r b j

For each trip origin o i and destination d i​ Define binary indicators

δ i o r = 1 , i f o i ∈ A r 0 , o t h e r w i s e ; δ i d r = 1 , i f d i ∈ A r 0 , o t h e r w i s e

Then the number of uncovered trip points becomes

U o r = ∑ i = 1 N 1 − δ i o r , U d r = ∑ i = 1 N 1 − δ i d r

Percentage of unserved trips (gap metrics)

G a p o r = U o r N , G a p d r = U d r N

For sensitivity analysis and marginal gain given buffer levels r k K k = 1 w h e r e r k < r k + 1

To define the marginal reduction in unserved trips

Δ o r k = G a p o r k − G a p o r k + 1 , Δ d r k = G a p d r k − G a p d r k + 1

Then the rate of decay of marginal improvement as a second-order sensitivity

∇ 2 G a p o r k = Δ o r k − Δ o r k + 1 , ∇ 2 G a p d r k = Δ d r k − Δ d r k + 1

In Phase 2, trips that both originated and terminated outside all GTFS-defined buffer zones were isolated to identify areas with no fixed-route transit access. These “orphan trips” represent concentrated pockets of unmet mobility demand. To spatially cluster these trips, the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithm was applied due to its capacity to discover natural groupings of varying shapes and densities without requiring a predefined number of clusters. This approach allowed for a data-driven delineation of high-need areas. To contextualize the clusters, the analysis was further enriched with supplementary spatial layers, including land use data, socio-demographic characteristics (e.g., median income, disability prevalence), and accessibility indicators.

Let.

• X = {x ₁, x ₂, …, x _n}: Set of spatial points representing orphan DRT trips
• xᵢ ∈ ℝ²: Each point defined by latitude and longitude coordinates.
• ε: Maximum distance threshold to consider two points as neighbors (spatial proximity threshold).
• MinPts: Minimum number of points within the ε-neighborhood required to form a dense region (cluster).

ε − neighborhood of point x i , N ε x i = x j ∈ X ∣ ∥ x i − x j ∥ ≤ ε

∣ N ε x i ∣ ≥ M i n P t s

x j ∈ N ε x i a n d ∣ N ε x i ∣ ≥ M i n P t s

C k = x i ∈ X ∣ ∃ x j ∈ C k s u c h t h a t x i i s d e n s i t y − r e a c h a b l e f r o m x j

∣ N ε x i ∣ < M i n P t s a n d x i i s n o t d e n s i t y − r e a c h a b l e f r o m a n y c o r e p o i n t

The effectiveness of density-based spatial clustering using DBSCAN is fundamentally dependent on the appropriate specification of its two hyperparameters: the neighborhood radius (ε) and the minimum number of points required to form a core cluster (MinPts). Improper parameterization can lead to either artificial fragmentation of demand patterns or excessive aggregation that obscures meaningful spatial heterogeneity. To ensure methodological rigor, reproducibility, and planning relevance, both parameters were selected through a structured, multi-step procedure combining statistical diagnostics, sensitivity analysis, and transit accessibility considerations.

The ε parameter was initially identified using a k-distance method, in which distances to each observation’s 4th nearest neighbor were computed and ranked in ascending order. The resulting k-distance plot exhibits a pronounced inflection point separating dense spatial structures from background noise, indicating a natural transition in spatial density. This elbow corresponds to an approximate distance of 0.25 miles and was selected as the optimal ε threshold.

This distance is not arbitrary; it aligns with empirically supported walk-accessibility thresholds commonly adopted in demand-responsive transit, microtransit, and shared pick-up point design. Unlike conventional fixed-route planning—where a 0.5-mile walk radius is often assumed—shared pick-up systems impose stricter access constraints due to user time sensitivity, physical limitations, and trip-purpose urgency. Accordingly, a 0.25-mile threshold represents a conservative yet operationally realistic upper bound for walk-accessible aggregation of DRT demand, particularly for equity-sensitive populations such as individuals with disabilities or limited vehicle access.

To evaluate the robustness of the selected ε value, a sensitivity analysis was conducted by systematically varying ε over a range of candidate values (0.10–0.40 miles), as illustrated in Figure 2. The results show that the number of clusters remains stable across a broad interval (0.15–0.30 miles), indicating strong structural consistency in the underlying demand patterns. At smaller ε values (<0.20 miles), clustering becomes overly fragmented, generating a higher proportion of noise points and failing to capture coherent demand pockets. In contrast, larger ε values (≥0.35 miles) lead to over-aggregation, merging spatially distinct demand concentrations and reducing the granularity required for localized service planning. The selected ε = 0.25 miles lies squarely within this stability plateau, balancing cluster cohesion and noise suppression.

Building on these identified clusters, Phase 3 introduced a prioritization model to rank zones according to a balance of operational demand and social equity considerations. A composite Equity-Demand Index was calculated for each zone by normalizing and weighting variables such as trip density, car ownership, income level, and disability rates. This multi-criteria framework produced a transparent and reproducible prioritization score for each zone, resulting in a Priority Score Map and a Ranked Zone List to guide targeted DRT deployment.

The study area is segmented into Z = {z1​,z2​,…,zm​}, where each zone Zi corresponds to a spatial cluster detected in Phase 2

Each zone is evaluated based on (p) normalized indicators.

• Ti ​: Trip density (orphan DRT trips per unit area in zone Zi​)
• Vi: Vehicle ownership rate (inversely related to transit dependency)
• Ii ​: Median income (negatively associated with transit equity needs)
• Di: Disability prevalence (percentage of population with mobility limitations)

Normalize each variable using Min-Max scaling:where X i represents the observed value for zone i, and X min and X max denote the minimum and maximum values across all clusters.

X ^ i = X i − min ⁡ x max x − min ⁡ x f o r X ∈ T , 1 V , 1 I , D

For indicators negatively associated with vulnerability (e.g., median income, vehicle ownership), reverse normalization was applied to ensure directional consistency with equity needs.

Assign weights w T , w V , w I , w D w i t h ∑ w j = 1 based on the analytic hierarchy process (AHP)

E I D i = w T . T i ^ + w v . 1 V i ^ + w I . 1 I i ^ + w D . D i ^

Weights were determined using the Analytic Hierarchy Process (AHP), incorporating expert judgment to reflect the relative importance of demand intensity and socio-demographic vulnerability. Pairwise comparisons were conducted to prioritize indicators associated with transit dependency. The resulting weights were applied consistently across clusters to compute the composite Priority Score Index.

To assess the stability of the prioritization framework, an alternative equal-weight specification was tested. The resulting cluster rankings demonstrated strong consistency with the AHP-weighted results, indicating that the prioritization outcomes are not highly sensitive to the weighting scheme.

In Phase 4, mobility flows between zones were modeled using origin-destination matrices derived from the DRT trip data. Desire line mapping was employed to visualize high-volume corridors, while zones with substantial inbound and outbound trip flows were identified as potential “Super-Hubs.”

Let O = o i j ∈ N m * m Denote the origin-destination matrix, where:

• Oij​: number of trips from zone Zi​ to zone Zj over a given period.

Total mobility score M i = ∑ j ≠ i o i j + ∑ j ≠ i o j i

A zone Zi is designated a Super-Hub if M i ≥ μ M + α · σ M

Where.

• μ m : mean of Mi across all mmm zones
• σ M : standard deviation of Mi
• α: threshold parameter

desire line vector set: D = z i , z j , o i j ∣ o i j > θ Where θ is a user-defined volume threshold

Based on the origin–destination flow analysis, clusters were evaluated for their network centrality using the total mobility score M i, defined as the sum of inbound and outbound DRT flows. Clusters exceeding the threshold M i ≥ μ + α σ, where μ and σ denote the mean and standard deviation of mobility scores across all clusters and α is a tuning parameter, were designated as Super-Hubs. Applying this criterion identifies a subset of high-performing clusters that concentrate a disproportionate share of inter-zonal travel. These Super-Hubs function as strategic transfer and coordination nodes within a hybrid fixed-route–DRT system, serving as logical anchor points for timed transfers, shared pick-up locations, and service consolidation. Their identification provides an operational mechanism for integrating flexible demand-responsive services with the fixed-route network while maximizing connectivity and system-wide efficiency.

Analysis and discussion

To initiate the spatial analysis, an exploratory diagnostic map was developed to compare the spatial distribution of fixed-route public transit stops with actual mobility demand captured through Demand-Responsive Transit (DRT) trip data. As visualized in Figure 3. This overlay reveals critical insights into the current limitations of the public transit network.

The concentration of fixed route stops in the urban core, particularly in central Kalamazoo, emphasizes the contrast with the widespread dispersion of DRT trips. Many demand points extend well beyond traditional service areas, reaching into low-density suburban, exurban, and rural regions. These outlying areas often have little to no overlap with fixed-route infrastructure, highlighting the existence of transit deserts areas with populations that are unserved or underserved. This spatial mismatch between transit supply and latent demand indicates that the current fixed-route system does not sufficiently address the distributed mobility needs of the population, especially among those with limited access to private vehicles.

To thoroughly assess the spatial alignment between fixed-route transit infrastructure and observed travel demand, a multi-scale buffer analysis was performed using incremental distances from 0.1 to 0.5 miles. These thresholds were chosen to represent different assumptions about pedestrian willingness to access transit services, with 0.5 miles widely accepted as the industry standard for walkable accessibility. For each distance increment, circular buffers were generated around all fixed-route bus stops defined in the GTFS dataset. These layered buffers enabled a sensitivity analysis to assess how coverage evolves with increasing walk distances.

The service areas generated were spatially overlaid with Demand-Responsive Transit (DRT) trip data, comprising both origin and destination points recorded over a 1-month period, to calculate the share of trips falling outside the service envelope at each buffer level. Figure 4 illustrates the spatial extent of the 0.5-mile buffer, which provides substantial coverage within the urban core of Kalamazoo.

Figure 5 illustrates the results of a multi-scalar buffer sensitivity analysis quantifying spatial transit accessibility as a function of pedestrian catchment thresholds. The conventional 0.5-mile isochrone—commonly adopted as a proxy for maximum walkability—encompassed a substantial portion of Kalamazoo’s urban transit service area. Nevertheless, 22.9% of DRT-originating events and 21.9% of destination points remained outside these fixed-route service envelopes, indicating a measurable service void in peripheral geographies. At the minimal 0.1-mile threshold, the analysis revealed that over half of DRT trip endpoints fell outside any buffer, underscoring the acuteness of first-mile/last-mile disconnects under constrained pedestrian tolerances. Critically, the delta in coverage gains between successive buffer increments exhibited rapid attenuation beyond 0.2 miles, reflecting diminishing marginal returns in spatial coverage efficiency. This inflection suggests that further densification of stop placement yields minimal accessibility dividends in low-density environments, thereby challenging the scalability of fixed-route transit alone. Consequently, these spatial asymmetries underscore the need for demand-responsive mobility frameworks to address structural inaccessibility and equitably expand service reach across heterogeneous urban and exurban landscapes.

To move beyond spatial clustering and into actionable, equity-informed planning, we introduced a multidimensional prioritization framework designed to uncover not only where demand exists but also who it represents and why it matters. Recognizing that not all demand holds the same value, we developed a customized Priority Score Index. This composite metric combines operational demand and social vulnerability indicators, including low income, disability prevalence, and the share of working-age population. Each of the 27 clusters identified through DBSCAN was scored using normalized and weighted variables, enabling a data-driven and reproducible ranking of zones based on their strategic importance for DRT deployment. To support and contextualize this framework, a composite visual Figure 6 was created, integrating four thematic heatmaps: DRT trip density, population density, median income, disability percentage, and working-age demographics.

Figure 7 Visualizes the output of the DBSCAN clustering process, presenting 27 uniquely colored spatial clusters of unserved Demand-Responsive Transit (DRT) trips across Kalamazoo County, with inter-cluster connections depicted by green flow lines. These organically formed clusters, derived solely from trip origin-destination coordinates beyond fixed-route walkable buffers, reveal concentrated pockets of unmet mobility demand across diverse geographies—from dense urban peripheries to remote rural edges. Each numbered cloud reflects a distinct high-priority zone identified by DBSCAN, serving as the spatial foundation for equity-informed analysis. The flow connections not only illustrate the intensity of inter-cluster travel behavior but also highlight latent mobility corridors currently unserved by traditional transit infrastructure. When linked to the Priority Score Index and socio-demographic diagnostics, for example, Cluster 15s high disability rate and Cluster 7’s low-income, car-limited population, this visual becomes a powerful planning tool, merging spatial clustering with social vulnerability to inform targeted, justifiable DRT deployment strategies.

To guide strategic transit planning and prioritize service expansion, Table 2 provides a ranked summary of the 27 clusters identified through DBSCAN analysis based on the Priority Score Index. Each cluster consolidates unmet Demand-Responsive Transit (DRT) trip demand and overlays it with key socio-demographic indicators, including median income, poverty rates, and populations with disabilities. This combined view enables a nuanced understanding of where mobility gaps are most pronounced and which areas require immediate attention. High-priority clusters, such as Cluster 27 and Cluster 2, not only exhibit dense DRT activity but also intersect with higher levels of social vulnerability, making them prime candidates for improved fixed-route service or hybrid DRT integration.

TABLE 2. Priority scores of DBSCAN-Derived clusters of unserved DRT demand.

To complement the quantitative prioritization, qualitative inspection of the highest-ranked clusters reveals consistent physical and land-use characteristics that explain their classification as transit deserts. Clusters 27, 2, and 15 are predominantly located in low-density residential or mixed-use zones characterized by discontinuous sidewalk infrastructure, limited pedestrian connectivity, and fragmented street networks. These areas often lack direct access to arterial corridors served by fixed-route transit and are separated from major activity centers such as employment hubs, healthcare facilities, and commercial services. In several cases, curvilinear street layouts and zoning patterns further constrain the feasibility of fixed-route extensions. Despite these structural barriers, the concentration of DRT trips indicates persistent latent demand, underscoring the role of these clusters as priority zones where conventional transit supply is misaligned with observed mobility needs.

The temporal distribution of the 2,337 unserved DRT trips identified across priority clusters was analyzed to understand peak demand periods better and inform service planning. As illustrated in Figure 8, which mirrors the temporal pattern observed in October 2019, approximately 82% of these unmet trips occurred on weekdays, totaling around 1,916 trips, while the remaining 18%, or roughly 421 trips, were recorded on weekends. Weekday demand exhibited distinct peaks during traditional commuting hours, particularly around 8:00 a.m. and 2:30 p.m., indicating a strong need for mobility support during work and school transitions. In contrast, weekend demand was more evenly distributed with a modest afternoon peak.

It is also important to contextualize the temporal scope of the DRT data used in this analysis. The trip records were collected during October 2019, prior to the COVID-19 pandemic, thereby avoiding behavioral distortions associated with lockdowns or service disruptions. October represents a transitional period with generally stable weather conditions and typical weekday activity patterns, making it well suited for capturing baseline demand for demand-responsive services. While absolute demand levels may vary across seasons, the spatial configuration of unmet demand and the relative prioritization of high-need clusters are expected to remain structurally consistent. Accordingly, although the magnitude of observed trips should not be extrapolated directly to other periods, the clustering outcomes and equity-based prioritization framework developed in this study remain robust and transferable beyond the specific study window.

Conclusion

This analysis emphasizes the urgent need for a more adaptable, inclusive, and data-driven approach to transit planning in Kalamazoo County. By incorporating spatial diagnostics, buffer sensitivity analysis, socio-demographic overlays, and temporal trip patterns, the study highlights clear gaps in the fixed-route transit system, especially in low-density suburban and rural areas where a large portion of mobility needs remain unmet. The DBSCAN clustering method identified 27 naturally formed zones of unmet demand, each with its own “mobility personality” defined not only by trip volume but also by indicators of vulnerability such as low income, disability rates, and limited vehicle access. These clusters provide a strong spatial foundation for prioritizing future Demand-Responsive Transit (DRT) efforts.

Furthermore, the Priority Score Index translated complex operational and equity variables into an actionable ranking system, assisting stakeholders in allocating resources where social returns are likely to be highest. Temporal demand analysis further revealed that unmet mobility is not randomly distributed throughout the week; instead, it is heavily concentrated during weekday peak periods, emphasizing the need for time-sensitive service designs, especially for work and school commuters.

These insights collectively establish a strategic basis for hybrid service models that combine fixed-route optimization with targeted DRT deployment. High-priority clusters such as Cluster 27, Cluster 2, and Cluster 15 should be considered early candidates for pilot programs or fixed-route extensions, especially where socio-economic indicators highlight the need for equitable mobility solutions. Ultimately, this integrated approach makes sure that public transportation investments are both efficient and responsive to spatial demand patterns, while also addressing the mobility needs of populations that have traditionally been underserved by conventional transit systems.

From an operational perspective, serving the identified high-priority clusters would require targeted allocation of demand-responsive transit resources rather than system-wide expansion. Given the observed trip densities and temporal concentration of demand, service provision could be achieved through modest fleet augmentation focused on peak periods, particularly in clusters with sustained weekday demand. While precise cost estimation depends on agency-specific parameters, prior DRT deployments suggest that concentrating vehicles in high-demand zones can reduce per-trip operating costs by improving vehicle utilization and minimizing deadheading. Accordingly, the prioritization framework presented in this study provides transit agencies with a practical basis for estimating fleet requirements, scheduling service windows, and evaluating cost–coverage trade-offs before implementation.

Recommendations and future work

To ensure that the findings of this study lead to tangible improvements for underserved populations, several targeted recommendations are proposed. First, transit agencies should prioritize launching hybrid mobility solutions—such as flexible DRT services or fixed-route extensions—within the highest-ranked clusters identified through the Priority Score Index. Clusters like 27, 2, and 15 not only demonstrate dense concentrations of unmet DRT trips but also intersect with populations showing high rates of poverty, disability, and limited vehicle access. Targeting these areas enables transit planners to maximize social impact while addressing structural service gaps. Second, the temporal analysis of unmet DRT trips reveals a clear weekday peak in demand, particularly around 8:00 a.m. and 2:30 p.m., aligning with typical commuting and school-related travel. Therefore, it is recommended that DRT service schedules be strategically aligned with these time windows to ensure timely and efficient service delivery. On weekends, demand is more evenly distributed, with a mild afternoon rise; flexible service models with adjustable routing could offer cost-effective coverage without compromising accessibility. Additionally, there is a critical need to bridge first-mile/last-mile gaps in peripheral zones just outside walkable catchments of fixed-route services. These areas, though near bus stops, remain functionally disconnected due to pedestrian limitations. Microtransit feeders, paratransit integration, and even non-motorized solutions, such as shared micromobility systems, could be explored to close these gaps. Furthermore, service planning should be based not only on operational data but also on socio-demographic metrics. By consistently incorporating variables such as disability prevalence, income levels, and car ownership rates into route and service allocation decisions, transit agencies can adopt a more equitable planning approach.

Future research should enhance this framework by integrating real-time data streams, such as AVL (Automatic Vehicle Location) and APC (Automated Passenger Counting), as well as mobile app trip requests, to enable dynamic DRT optimization. Utilizing machine learning algorithms, such as Gradient Boosted Trees, Long Short-Term Memory (LSTM) networks, or Graph Neural Networks (GNNs), could enhance demand forecasting, spatial clustering, and route planning by leveraging temporal patterns and social vulnerability overlays. Additionally, reinforcement learning could be applied to create adaptive dispatch strategies that respond to changing demand and network conditions. Multi-objective optimization models that balance cost, coverage, and equity can help simulate service expansion scenarios within budget constraints. Finally, incorporating GIS-based multi-criteria decision analysis (MCDA) would aid in spatial prioritization by combining socio-economic, land-use, and transportation data to guide future DRT deployments more effectively and fairly.

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Footnotes

Edited by: Omar Darwish, Eastern Michigan University, United States

Reviewed by: Shorouq Al-Eidi, Tafila Technical University, Jordan

Majdi Maabreh, Hashemite University, Jordan