Evolution of weighted complex bus transit networks with flow

Study on the intrinsic properties and evolutional mechanism of urban public transit networks (PTNs) has great significance for transit planning and control, particularly considering passengers' dynamic behaviors. This paper presents an empirical analysis for exploring the complex properties of Beijing's weighted bus transit network (BTN) based on passenger flow in L-space, and proposes a bi-level evolution model to simulate the development of transit routes from the view of complex network. The model is an iterative process that is driven by passengers' travel demands and dual-controlled interest mechanism, which is composed of passengers' spatio-temporal requirements and cost constraint of transit agencies. Also, the flow's dynamic behaviors, including the evolutions of travel demand, sectional flow attracted by a new link and flow perturbation triggered in nearby routes, are taken into consideration in the evolutional process. We present the numerical experiment to validate the model, where the main parameters are estimated by using distribution functions that are deduced from real-world data. The results obtained have proven that our model can generate a BTN with complex properties, such as the scale-free behavior or small-world phenomenon, which shows an agreement with our empirical results. Our study's results can be exploited to optimize the real BTN's structure and improve the network's robustness.