A general phase transition model for vehicular traffic

Sebastien Blandin (1) , Dan Work (1) , Paola Goatin (2, 3) , Benedetto Piccoli (4) , Alexandre Bayen (1)

1 CEE - Department of Civil and Environmental Engineering [Berkeley]
2 IMATH - Institut de Mathématiques de Toulon - EA 2134
3 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
4 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"

An extension of the Colombo phase transition model is proposed. The congestion phase is described by a two-dimensional zone defined around an equilibrium flux known as the classical fundamental diagram. General criteria to build such a set-valued fundamental diagram are enumerated, and instantiated on several equilibrium fluxes with different concavity properties. The solution of the Riemann problem in the presence of phase transitions is obtained through the construction of a Riemann solver, which enables the definition of the solution of the Cauchy problem using wavefront tracking. The free-flow phase is described using a Newell-Daganzo fundamental diagram, which allows for a more tractable definition of phase transition compared to the original Colombo phase transition model. The accuracy of the numerical solution obtained by a modified Godunov scheme is assessed on benchmark scenarios for the different flux functions constructed.

Mots clés: Partial differential equations; Hyperbolic systems of conservation laws; Macroscopic highway traffic flow model; Phase transition; Numerical scheme; Riemann solver

Domaines: Equations aux dérivées partielles [math.AP]

Sebastien Blandin, Dan Work, Paola Goatin, Benedetto Piccoli, Alexandre Bayen. A general phase transition model for vehicular traffic. SIAM Journal on Applied Mathematics, 2011, 71 (1), pp.107-127. ⟨hal-00537268⟩