Congestions and spectral transitions in time-lagged correlations of motorway traffic

Abstract

The understanding of congestions contributes to the development of effective traffic management strategies. The propagation of congestions from a motorway section to the neighboring ones results in correlations. Here, we study symmetrized time-lagged correlation matrices and show how their spectral properties reveal congestion durations. We first carry out an empirical analysis of velocities for two local motorway networks, then set up a numerical simulation for indicator time series of traffic phases, and further propose a simplified, analytical model capturing various scenarios of congestion durations. Our empirical analysis reveals a transition behavior for the dominant eigenvalue as function of time lags, reflecting changes in traffic dynamics. Furthermore, both the numerical simulations and the analytical model disclose a nonlinear relation between the spectral transition and the congestion duration.