Determination of paratransit accessibility: A methodological and empirical study of the collective fixed-route minibus system in Djibouti city

Abstract

This thesis investigates the accessibility of collective fixed-route paratransit in Djibouti City and develops a methodological framework adapted to the realities of informal transport systems in developing urban contexts. In many African cities, public transportation networks are dominated not by formal bus or rail systems but by flexible, demand-driven paratransit services, typically operating without fixed stops, schedules, or regulatory oversight. These systems present structural complexities that conventional accessibility indices are not designed to address. The thesis, therefore, aims to redefine the measurement of accessibility in a way that captures the spatial, temporal, and behavioral attributes of paratransit networks, while remaining feasible in environments where data availability is limited. The study combines theoretical, methodological, and empirical components to produce a comprehensive and context-sensitive accessibility framework, which is then applied to Djibouti City. The thesis begins by tracing the evolution of the concept of accessibility, demonstrating how its definition has expanded from early notions of simple distance-based separation to multifaceted interpretations involving travel behavior, land-use interactions, and activity participation. Theoretical developments across decades reveal that accessibility cannot be reduced to a single dimension; instead, it reflects the complex interplay between mobility, opportunity distribution, time constraints, and user preferences. While various models have emerged, ranging from cumulative opportunity measures to gravity-based and time-dependent models, most assume the presence of fixed, scheduled public transport systems. Such assumptions make them unsuitable for informal systems like paratransit, where services lack fixed stations, waiting times vary unpredictably, and users' walking patterns reflect local tradeoffs in safety, land value, and convenience. This thesis positions itself within this theoretical gap by proposing tools that better capture real conditions in such contexts. A central contribution of this research is the development of a four-dimensional accessibility framework adapted to paratransit systems. The model integrates the paratransit network coverage ratio, walking time to service, waiting time at the station, and the opportunities accessible through the network. These dimensions reflect both physical access and the value of outcomes reached through transport. The framework is grounded in behavioral evidence: decay functions for walking and waiting times are calibrated using empirical data collected through extensive household surveys and on-site observations. This empirical grounding ensures that accessibility scores reflect actual user tolerances rather than arbitrary thresholds commonly imposed in other models. Two versions of the accessibility model are proposed: a single station approach, which identifies the best-performing station available to a section, and a multiple stations approach, which aggregates the accessibility contributions of all accessible stations. These two perspectives capture complementary dimensions of network use: the single station model reflects the optimal available option, while the multiple stations model captures cumulative network benefits and redundancy. To incorporate opportunities into the analysis, the thesis extends the basic accessibility model by introducing an opportunity factor. This factor quantifies the number of reachable educational, health, and shopping facilities and weights them based on the distribution of opportunities within the station-based paratransit network coverage area. Opportunities are defined not merely by their presence but by their user volumes, thus recognizing the varying levels of demand across facilities. By integrating opportunities into both the single and multiple stations models, the analysis moves beyond access to the system and instead reflects its capacity to connect residents to meaningful activities. The empirical application focuses on Djibouti City, the capital and largest urban center in Djibouti. The city is divided into 120 statistical sections, of unequal shapes and sizes, which serve as the spatial unit of analysis. Paratransit constitutes the dominant mode of public transport, operating along ten primary lines with significant route overlaps. Although those lines cover a combined physical route length of approximately 67 km, several lines share the same corridors, reducing effective geographic coverage. At the same time, the majority of the city's population is concentrated near these corridors, reflecting the structural relationship between informal transit service provision, residential density, and land-use patterns. To evaluate accessibility, the study first determines the paratransit network coverage area, representing the region accessible within a tolerable walking time. Based on survey responses from more than 1,600 users, the third quartile of walking times (which was found to be 8 minutes) is adopted as the threshold for coverage, recognizing that in developing cities, users commonly walk longer distances to reach transport services. Using this threshold, the paratransit network is found to cover 24.23 km² (only 39.5% of the urban area), yet this area contains nearly 77% of the city's population. This spatial imbalance highlights the implications of informal and profit-driven network design: operators concentrate service in high-density corridors, while peripheral neighborhoods remain underserved. Using a questionnaire and observation, the study established a calibrated decay function for walking and waiting time using the complementary cumulative distribution function. The Walking time to the paratransit line for each section is then calculated using GIS-based network analysis, measuring pedestrian travel times from section centroids to the closest accessible route. The waiting time at stations is determined based on the average waiting time observed in each location. For both walking and waiting time, the one-parameter Gaussian model was found to be the one that captures the gradual decline in user tolerance as walking and waiting time increase, aligning well with empirical patterns while retaining mathematical simplicity. Application of the single station accessibility model reveals strong disparities in spatial access across Djibouti City. More than 60% of the city's land area falls into the "No Access" or "Very Poor" categories, although these areas contain about 28% of the population. Accessibility is highest in compact central neighborhoods served by multiple paratransit lines and characterized by short walking and waiting times. The theoretical maximum accessibility score of 100% is rarely achieved, as no section combines full coverage with zero travel and waiting time. Under this model, the highest observed accessibility is approximately 80.5%. In contrast, the multiple stations model yields systematically higher accessibility scores, as it accounts for cumulative benefits. The mean accessibility increases from approximately 49% (single station) to 81% (multiple stations). Despite this increase, disparities persist: more than 60% of the urban land area remains within the lowest two categories of accessibility (with a population of 28%). The high cumulative scores in central districts reflect the convergence of several paratransit lines along shared corridors, offering redundancy and flexibility even in the absence of formal route planning. Incorporating opportunities into the analysis provides an even more detailed picture. A comprehensive dataset of 223 opportunity facilities (including schools, health centers, and shopping facilities) was collected and geolocated using field surveys. These facilities represent a total of 130,097 opportunity units based on student counts, patient consultations, and customer flows. Approximately 83% of facilities fall within the paratransit coverage area; however, some of the largest institutions, including the main university campus, remain outside the network's reach. The integration of opportunity factors into the accessibility models reveals that even though central districts enjoy high spatial and temporal accessibility, not all high-demand corridors connect effectively to essential destinations. When opportunities are included, more than 74% of the city's land area still falls into the "No Access" or "Very Poor Access" categories. This finding underscores the importance of evaluating not just the reachability of the network, but connectivity to meaningful destinations. Across all models, spatial inequity emerges as a consistent theme. Peripheral districts suffer from inadequate coverage, long walking times, and limited connectivity. By contrast, central areas, particularly those lying along a north-south corridor, demonstrate high accessibility due to their closeness to overlapping paratransit routes. The analysis suggests that paratransit, despite its informality, plays a critical role in structuring urban form and shaping residential location choices. Moreover, the concentration of lines along a few corridors highlights the lack of coordinated service planning and the tendency of private operators to prioritize profitable routes over equitable coverage. In conclusion, this thesis demonstrates that measuring accessibility in informal paratransit systems requires rethinking traditional models and tailoring them to behavioral realities, local mobility patterns, and data constraints. The proposed framework advances academic understanding and supports practical decision-making. Ultimately, it highlights that accessibility is not merely about physical proximity to transport, but about ensuring that all residents can reliably and affordably reach essential opportunities. Through its methodological innovations and empirical insights, the thesis contributes to the broader objective of shaping more equitable, efficient, and inclusive transport systems in Djibouti and comparable cities across the Global South.