A game theoretic macroscopic model of lane choices at traffic diverges with applications to mixed–autonomy networks

Vehicle bypassing is known to increase delays at traffic diverges. However, due to the complexities of this phenomenon, accurate and yet simple models of such lane change maneuvers are hard to develop. In this work, we present a macroscopic model for predicting the number of vehicles that perform a bypass at a traffic diverge when taking an exit link. We interpret the bypassing maneuver of vehicles at a traffic diverge as drivers acting selfishly; every vehicle selects lanes such that its own cost of travel is minimized. We discuss how we model the costs that are incurred by the vehicles. Then, taking into account the selfish behavior of vehicles, we model the lane choice of vehicles at a traffic diverge as a Wardrop equilibrium. We state and prove the properties of the equilibrium in our model. We show that there always exists an equilibrium for our model. Moreover, although our model is an instance of nonlinear asymmetrical routing games which in general have multiple equilibria, we prove that the equilibrium of our model is unique under certain assumptions that we observed to hold in all our case studies. We discuss how our model can be calibrated by running a simple optimization problem. Then, using our calibrated model, we validate it through simulation studies and demonstrate that our model successfully predicts the aggregate lane change maneuvers that are performed by vehicles at a traffic diverge. Having shown the predictive power of our model, we discuss how our model can be employed to obtain the optimal lane choice behavior of vehicles, where the social or the overall cost of all vehicles is minimized. Finally, we demonstrate how our model can be utilized in scenarios where a central authority can dictate the lane choice and trajectory of certain vehicles, for example autonomous vehicles directed by a central authority, so as to increase the overall vehicle mobility at a traffic diverge. Examples of such scenarios include the case when both human driven and autonomous vehicles coexist in the network.