The Riemann Problem and Interaction of Waves for the Aw-Rascle Model with Variable Velocity Offset

We are concerned with the Riemann problem for the Aw-Rascle (AR) traffic flow model with variable velocity offset. The model describes the traffic flow under different road conditions. The stationary wave is introduced in the traffic flow, which is determined by an ordinary differential equation. The resonance phenomenon and coalescence of waves are analyzed. Uniqueness of the Riemann solution is also discussed. We further study the interaction of elementary waves case by case, under the framework of the characteristic analysis method. Numerical simulations are also given to verify our analysis.