Macroscopic modeling of lane‐changing for two‐lane traffic flow

We propose a macroscopic model of lane‐changing that is consistent with car‐following behavior on a two‐lane highway. Using linear stability theory, we find that lane‐changing affects the stable region and the propagation speeds of the first‐order and second‐order waves. In analyzing a small disturbance, our model effectively reproduces certain non‐equilibrium traffic‐flow phenomena—small disturbance instability, stop‐and‐go waves, and local clusters that are affected by lane‐changing. The model also gives the flow‐density relationships in terms of the actual flow rate, the lane‐changing rate, and the difference between the potential flow rate (the flow rate that would have occurred without lane‐changing) and the actual flow rate. The relationships between the actual flow rate and traffic density and between the lane‐changing rate and traffic density follow a reverse‐lambda shape, which is largely consistent with observed traffic phenomena.