Multiple abrupt phase transitions in urban transport congestion

During the last decades, the study of cities has been transformed by new approaches combining engineering and complexity sciences. Network theory is playing a central role, facilitating the quantitative analysis of crucial urban dynamics, such as mobility, city growth or urban planning. In this framework, betweenness, a well-known centrality measure, represents a fundamental tool, standing out as a proxy of traffic density and congestion. In this work, we focus on the spatial aspects of congestion. Analyzing a large amount of real city networks, we show that most cities present a set of congestion regimes, separated by abrupt transitions. To help unveiling this spatial dependence of the betweenness, we introduce a simple model composed of a grid connected to a set of tree graphs. This structure, coined as the GT-model, allows us to analytically describe in terms of betweenness, how and why congestion emerges in particular geographical areas of monocentric cities. The model predicts the emergence of several congestion regimes, with abrupt transitions between them, related to the entanglement of arterial and urban local roads. The existence of these regimes and transitions is in agreement with the multiple abrupt phase transitions found for real cities, and represents an important step towards the understanding and optimization of traffic dynamics over coupled road networks.