A Second Order Traffic Flow Model with Lane Changing

This paper concerns modeling and computation of traffic flow for a single in-lane flow as well as multilane flow with lane changing. We consider macroscopic partial differential equation models of two types: (i) First Order Models : equilibrium models, scalar models expressing car mass conservation; and (ii) Second Order Models : dynamic models, 2 × 2 hyperbolic systems expressing mass conservation as well as vehicle acceleration rules. A new second order model is proposed in which the acceleration terms take lead from microscopic car-following models, and yield a nonlinear hyperbolic system with viscous and relaxation terms. Lane changing conditions are formulated and mass/momentum inter-lane exchange terms are derived. Numerical results are shown, illustrating the merit of the models in describing a rich array of realistic traffic scenarios including varying road conditions, lane closure, and stop-and-go flow patterns.