  Understanding the mechanisms leading to the formation and the propagation of
traffic jams in large cities is of crucial importance for urban planning and
traffic management. Many studies have already considered the emergence of
traffic jams from the point of view of phase transitions, but mostly in simple
geometries such as highways for example, or in the framework of percolation
where an external parameter is driving the transition. More generally,
empirical evidence and characterization for a congestion transition in complex
road networks is scarce, and here we use traffic measures for Paris (France)
during the period 2014-2018 for testing the existence of a jamming transition
at the urban level. In particular, we show that the correlation function of
delays due to congestion is a power law (with exponent $\eta\approx 0.4$)
combined with an exponential cut-off $\xi$. This correlation length $\xi$ is
shown to diverge during rush hours, pointing to a jamming transition in urban
traffic. We also discuss the spatial structure of congestion and identify a
core of congested links that participate in most traffic jams and whose
structure is specific during rush hours. Finally, we show that the spatial
structure of congestion is consistent with a reaction-diffusion picture
proposed previously.
