Study of Cross-Correlations in Traffic Networks with Applications to Perimeter Control

A cross-correlation is proposed between network-aggregated density and flow as a natural indicator of traffic phases for two-dimensional road networks. An online estimator of the cross-correlation was studied with the use of empirical data. The result suggests that the measure can be used to identify traffic phases. To understand better the behavior of the true statistical cross-correlation, generic networks were simulated. With homogeneously distributed densities, the simulations suggested that the cross-correlation monotonically decreases with the growth of the mean density and vanishes when the network is at capacity. As a consequence, for such networks, the phase can be identified from a single point on the curve of the cross-correlation versus mean density. A case study of cross-correlation–based perimeter-control strategies was performed, with gate traffic flowing into the network when the cross-correlation was below a (negative) threshold to improve network flows. The simulation results suggest that even with anisotropic traffic demand, the cross-correlation–based control strategy can improve network performance, specifically traffic flow and density heterogeneity.