Interaction of elementary waves for the Aw-Rascle traffic flow model with variable lane width

In this paper, we consider the interaction of elementary waves for the Aw-Rascle (AR) traffic flow model with variable lane width. The model is established based on the conservation laws where the lane width is considered, and the variable spaces ahead of the vehicles can be viewed as a source term which is incorporated into the model. Stationary waves are involved as the ingredient of the elementary waves. We then discuss the interactions of stationary wave with rarefaction wave, shock wave and contact discontinuity respectively, and construct the solutions globally in the phase plane. The results may contribute to dealing with traffic jam problems in the future study.

Automated summary

This paper explores the interaction of elementary waves in the AR traffic flow model with variable lane width, discussing the interactions of stationary wave with rarefaction wave, shock wave, and contact discontinuity. Solutions are constructed globally in the phase plane, potentially aiding in addressing traffic jam issues in future studies.