An extended macroscopic model for traffic flow on curved road and its numerical simulation

In this paper, we propose a full angular velocity difference model by introducing the angular velocity and displacement on curved road. The relation of transformation of microscopic model in form of angular variables into macroscopic one is deduced. Consequently, a corresponding continuum traffic flow model on curved road is derived. The critical condition for the steady traffic flow is obtained. Meanwhile, the stability condition of this continuum traffic model is compared with one of the microscopic model and lattice hydrodynamic traffic model on curved road. By nonlinear analysis, the KdV–Burgers equation which describes the density wave near the neutral stability line is derived. Furthermore, the numerical simulations are carried out to verify the validity of this macroscopic traffic. Results indicate the radius of curved road have a great impact on the formation of traffic jams. Local clustering effects in the state of instability of traffic flow give rise to the stop&go traffic jams. Numerical simulation also indicates the unstable region is shrunken under the increasing strength of the angular velocity difference.

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