Freeway network design with exclusive lanes for automated vehicles under endogenous mobility demand

Automated vehicles (AV) have the potential to provide cost-effective mobility options along with overall system-level benefits in terms of congestion and vehicular emissions. Additional resource allocation at the network level, such as AV-exclusive lanes, can further foster the usage of AVs rendering this mode of travel more attractive than legacy vehicles (LV). However, it is necessary to find the crucial locations in the network where providing these dedicated lanes would reap the maximum benefits. In this study, we propose an integrated mixed-integer programming framework for optimal AV-exclusive lane design on freeway networks which accounts for commuters' demand split among AVs and LVs via a logit model incorporating class-based utilities. We incorporate the link transmission model (LTM) as the underlying traffic flow model due to its computational efficiency for system optimum dynamic traffic assignment. The LTM is modified to integrate two vehicle classes namely, LVs and AVs with a lane-based approach. The presence of binary variables to represent lane design and the logit model for endogenous demand estimation results in a nonconvex mixed-integer nonlinear program (MINLP) formulation. We propose a Benders' decomposition approach to tackle this challenging optimization problem. Our approach iteratively explores possible lane designs in the Benders' master problem and, at each iteration, solves a sequence of system-optimum dynamic traffic assignment (SODTA) problems which is shown to converge to fixed-points representative of logit-compatible demand splits. Further, we prove that the proposed solution method converges to a local optima of the nonconvex problem and identify under which conditions this local optima is a global solution. The proposed approach is implemented on three hypothetical freeway networks with single and multiple origins and destinations.