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It is understood that congestion in traffic can be interpreted in terms ofthe instability of the equation of dynamic motion. The evolution of a trafficsystem from an unstable or metastable state to a globally stable state bears astrong resemblance to the phase transition in thermodynamics. In this work, weexplore the underlying physics of the traffic system, by examining closely thephysical properties and mathematical constraints of the phase transitionstherein. By using a mesoscopic approach, one entitles the catastrophe model thesame physical content as in the Landau's theory, and uncovers its closeconnections to the instability of the equation of motion and to the transitionbetween different traffic states. In addition to the one-dimensionalconfiguration space, we generalize our discussions to the higher-dimensionalcase, where the observed temporal oscillation in traffic flow data isattributed to the curl of a vector field. We exhibit that our model canreproduce the main features of the observed fundamental diagram including theinverse-$\lambda$ shape and the wide scattering of congested traffic data. Whenproperly parameterized, the main feature of the data can be reproducedreasonably well either in terms of the oscillating congested traffic or interms of the synchronized flow.

A mesoscopic approach on stability and phase transition between different traffic flow states