Comparative empirical analysis of flow-weighted transit route networks in R-space and evolution modeling

Urban public transit system is a typical mixed complex network with dynamic flow, and its evolution should be a process coupling topological structure with flow dynamics, which has received little attention. This paper presents the R-space to make a comparative empirical analysis on Beijing's flow-weighted transit route network (TRN) and we found that both the Beijing's TRNs in the year of 2011 and 2015 exhibit the scale-free properties. As such, we propose an evolution model driven by flow to simulate the development of TRNs with consideration of the passengers' dynamical behaviors triggered by topological change. The model simulates that the evolution of TRN is an iterative process. At each time step, a certain number of new routes are generated driven by travel demands, which leads to dynamical evolution of new routes' flow and triggers perturbation in nearby routes that will further impact the next round of opening new routes. We present the theoretical analysis based on the mean-field theory, as well as the numerical simulation for this model. The results obtained agree well with our empirical analysis results, which indicate that our model can simulate the TRN evolution with scale-free properties for distributions of node's strength and degree. The purpose of this paper is to illustrate the global evolutional mechanism of transit network that will be used to exploit planning and design strategies for real TRNs.