Heterogeneity induced localization of traffic congestion on networks

The emergence of congestion is a critical phenomenon in transport systems. Transport is organized along pathways abstracted by links, which connect different nodes as regions to form the network. The modeling of traffic has so far mainly been based on one-dimensional lattices or networked queuing systems, which restricts mechanistic insights and analytical tractability for traffic dynamics on general networks. An interpretable kinetics model is necessary for understanding the impact of the network structure on traffic congestion in large-scale networks. Considering a generalized flow-density relation within each node, we propose and investigate a general traffic model on networks with external injections and exits. We observe various phases in terms of node density that exhibit distinct behaviors under different injection rates. The onset of congestion along with the coexistence of free nodes and congested nodes, manifested by the spatial localization of traffic congestion, is induced by the asymmetry of the flow transitions between neighbors in the network. The proposed congestion centrality allows us to determine the congestion threshold, identify congested nodes and predict congestion propagation. Our model and results are shown to cover a broad spectrum of implications for transport dynamics on networks as well as offer a practical prospect for traffic optimizations such as congestion alleviation and targeted diffusion.