  The Static User Equilibrium is a powerful framework for the theoretical study
of traffic. Despite the restricting assumption of stationary flows that
intuitively limit its application to real traffic systems, many operational
models implementing it are still used without an empirical validation of the
existence of the equilibrium. We investigate its existence on a traffic dataset
of three months for the region of Paris, FR. The implementation of an
application for interactive spatio-temporal data exploration allows to
hypothesize a high spatial and temporal heterogeneity, and to guide further
quantitative work. The assumption of locally stationary flows is invalidated in
a first approximation by empirical results, as shown by a strong spatial and
temporal variability in shortest paths and in network topological measures such
as betweenness centrality. Furthermore, the behavior of spatial autocorrelation
index of congestion patterns at different spatial ranges suggest a chaotic
evolution at the local scale, especially during peak hours. We finally discuss
the implications of these empirical findings and describe further possible
developments based on the estimation of Lyapunov dynamical stability of traffic
flows.
