Measuring route diversity for urban rail transit networks: A case study of the Beijing Metro Network

Most stations and tracks in metro networks are irreplaceable due to daily operations. If any of them were disrupted, it would impact not only the individual metro line but also the whole metro network. Therefore, metro managers need to have a good understanding of alternative routes between each pair of stations in the metro network. In the event of incidents, metro managers can make use of this information to reroute passengers to minimize the impact of disruptions. This paper aims to develop a route diversity index to address two questions: 'how many reasonable routes are there for passengers between any two stations in normal operations or in the event of a disruption ?' and 'which stations are most vulnerable (i.e., the largest impact to the overall metro network when they are disrupted)?' To implement this measure in practice, definitions of routes and route diversity and a solution algorithm based on characteristics of metro networks are described to calculate the route diversity index. To show proof of the concept, a simple network example and a real-world network based on the Beijing Metro network in China are presented to demonstrate the feasibility of the route diversity index and its application to a real-world metro network.