Title: A Game Theoretic Macroscopic Model of Bypassing at Traffic Diverges with Applications to Mixed Autonomy Networks,
Abstract: Vehicle bypassing is known to negatively affect 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 bypass
at a traffic diverge. We take into account the selfishness of vehicles in
selecting their lanes; every vehicle selects lanes such that its own cost is
minimized. We discuss how we model the costs experienced by the vehicles. Then,
taking into account the selfish behavior of the vehicles, we model the lane
choice of vehicles at a traffic diverge as a Wardrop equilibrium. We state and
prove the properties of Wardrop equilibrium in our model. We show that there
always exists an equilibrium for our model. Moreover, unlike most nonlinear
asymmetrical routing games, we prove that the equilibrium is unique under mild
assumptions. We discuss how our model can be easily calibrated by running a
simple optimization problem. 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 for bypassing at
a traffic diverge. We further discuss how our model can be employed to obtain
the optimal lane choice behavior of the vehicles, where the social or total
cost of 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 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. We show how
certain decisions of the central authority can affect the total delays in such
scenarios via an example.