Phase transition model of non-stationary traffic flow: Definition, properties and solution method

We consider the problem of modeling traffic phenomena at a macroscopic level. Increasing availability of streaming probe data allowing the observation of non-stationary traffic motivates the development of models capable of leveraging this information. We propose a phase transition model of non-stationary traffic in conservation form, capable of propagating joint measurements from fixed and mobile sensors, to model complex traffic phenomena such as hysteresis and phantom jams, and to account for forward propagation of information in congested traffic. The model is shown to reduce to the Lighthill–Whitham–Richards model within each traffic phase for the case of stationary states, and to have a physical mesoscopic interpretation in terms of drivers’ behavior. A corresponding discrete formulation appropriate for practical implementation is shown to provide accurate numerical solution to the proposed model. The performance of the model introduced is assessed on benchmark cases and on experimental vehicle trajectories from the NGSIM datasets.

► Definition of a phase transition flow model with perturbation variable in congestion. ► Construction of the integral curves of the model and definition of a Riemann solver. ► Design of a numerical discretization scheme with meaningful physical interpretation. ► Comparative performance assessment of phase transition model on real trajectory data. ► Analysis of modeling capabilities of the model on test and experimental data.