Congestions and Spectral Transition in Time-Lagged Correlations of Motorway Traffic

The congestion of a motorway section is propagated to its neighbouring sections, leading to correlations. The resulting correlation matrix encodes the information on congestion. Here, we study symmetrized time-lagged correlations and show how their spectral properties reveal congestion durations. We carry out an empirical analysis and find a transition behavior for the dominant eigenvalue as function of the time lag. Furthermore, we set up a numerical simulation model for indicator time series of traffic phases as well as a simplified model that we treat analytically. We consider various scenarios. Our results reveal a nonlinear relation between the spectral transition and the congestion duration. In our simplified model, we derive this relation analytically.