A Game-Theoretic Model for Aggregate Lane Choice Behavior of Highway Mainline Vehicles at the Vicinity of On-ramps

Highway on-ramps are regarded as a typical traffic scenario that may lead to congestion in modern transportation systems. On-ramp vehicles need to merge into the mainline traffic whereas through vehicles on the mainline intend to travel across the potential merging area with the least effort. Mainline through vehicles on the lane closest to the on-ramp, to minimize their own effort, either stay steadfast on this outermost lane and prepare to merge with on-ramp vehicles, or they change to a lane further from the on-ramp and bypass the potential merging area. The lane-changing choice is known to be difficult to model and through vehicles acting selfishly may force on-ramp vehicles to take dangerous merging maneuvers and then compromise the safety and efficiency of the highway. In this work, we model the aggregate lane choice behavior of highway mainline vehicles facing on-ramps ahead. We propose a model for the costs that the vehicles on the highway mainline evaluate when they choose their lanes at the vicinity of on-ramps. Assuming all vehicles choose their lanes selfishly, we model the resulting aggregate lane choice behavior of the mainline vehicles as a Wardrop equilibrium. We prove that the equilibrium exists and is unique. We then validate our model using micro-scale traffic simulation data. Moreover, we model mainline vehicles' socially optimal lane choice behavior. We conclude that the social traffic conditions will be improved if mainline vehicles are encouraged to steer to an adjacent lane further from the on-ramp and give away more space to on- ramp vehicles.