Prediction of traffic convective instability with spectral analysis of the Aw–Rascle–Zhang model

• We linearize and diagonalize the ARZ model. We give a Froude number for traffic.
• Spectral domain transfer functions are derived and decompose the model.
• The linearized system is convectively unstable in the free-flow regime.
• We conduct experiments with the linearized model on the NGSIM dataset.
• We show that the linearization does not destroy the accuracy of the model.

This article starts from the classical Aw–Rascle–Zhang (ARZ) model for freeway traffic and develops a spectral analysis of its linearized version. A counterpart to the Froude number in hydrodynamics is defined that enables a classification of the nature of vehicle traffic flow using the explicit solution resulting from the analysis. We prove that our linearization about an equilibrium is stable for congested regimes and unstable otherwise. NGSIM data for congested traffic trajectories is used so as to confront the linearized model's predictions to actual macroscopic behavior of traffic. The model is shown to achieve good accuracy for speed and flow. In particular, it accounts for the advection of oscillations on boundaries into the interior domain where the PDE under study is solved.