Benders' decomposition for freeway network design under endogenous automated mobility demand

Automated vehicles (AV) have the potential to provide cost-effective mobility options along with 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). We propose an integrated mixed-integer programming framework for optimal AV-exclusive lane design on a freeway network which accounts for commuters' demand split among AVs and LVs via a logit model. 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 two hypothetical freeway networks with single and multiple origins and destinations. Our numerical results reveal that the optimal lane design of freeway network is non-trivial and can inform on the value of accounting for endogenous demand in the proposed freeway network design.