A Reaction-Diffusion Model for Congestion Propagation in Urban Networks

While cascade phenomena have been broadly studied by physicists, understanding and modeling of congestion propagation in large urban city networks still remains a challenge. Most efforts are mainly based on micro-simulations of link-level traffic dynamics without a proper treatment of physical laws. The main purpose of this paper is to reveal the process of congestion formation by exploring empirical and simulated data from large-scale urban networks. Specifically, the authors aim at studying the spatiotemporal relation of congested links, observing congestion propagation from an macroscopic perspective, and develop a dynamic model with a few number of parameters that can properly reproduce the spatiotemporal distribution of congestion and cascade phenomena of traffic. The model is based on two ingredients: a reaction and a diffusion term. The interaction of these two terms brings the model in a self-organized pattern that after appropriate calibration can reproduce realistic traffic scenarios. Vehicles spread through the urban network by diffusion as well as the values of average link speed according to a Fundamental Diagram that relies on density, flow and speed [(1), (2)]. The reaction term will be the responsible of any exoge- nous change of concentration of vehicles, e.g. exogenous demand. The combination of these two terms will reproduce many different traffic scenarios. The results presented show very good data matching with an available data set of more than 20k taxis global positioning system (GPS) in Shenzhen during the morning peak hour.