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.