Measuring route diversity in spatial and spatial-temporal public transport networks

Route diversity is a pivotal metric for evaluating the redundancy of transportation networks, a fundamental aspect of system resilience. This study provides a comprehensive exploration of route diversity in multimodal public transport systems, specifically considering the unique characteristics of bus networks. Our research introduces a two-pronged approach to measuring route diversity within spatial public transport networks, delving into service-based and infrastructure-based perspectives. The former assesses redundancy against transit service disruptions by factoring in transit line overlaps, while the latter evaluates redundancy against infrastructure-related interruptions by considering overlapping road segments on which transit lines rely. In addition, the study advances by modelling public transport systems as multilayer spatial-temporal networks, integrating time-variable service frequency and travel time uncertainty, which enables us to derive route diversity for origin-destination (O-D) pairs across different time periods. We present a case study of the multimodal public transport network in Jiading District, Shanghai, revealing a power-law distribution of the route diversity. The results unveil O-D pairs with lower route diversity, underscoring their lack of resilience against various disturbances. Lower service-based route diversity suggests the necessity of enhancing service frequency and bolstering cross-line combined transit scheduling, while lower infrastructure-based route diversity could warrant the design of road-diversified transit lines, especially within bus corridors. Besides, relative route diversity between the two indices highlights specific O-D pairs with notable disparities in service and infrastructure redundancy. This difference is correlated with the distance between O-D pairs and the road network's configuration. This analysis underscores the method's potential to offer more relevant insights to public transport planners and operators for adjusting transit lines and schedules through a resilience-focused lens.