Joint lane management and signal optimization for mixed-autonomy intersections: An analytical approach

Lane management approaches have been extensively studied as effective strategies for managing mixed-autonomy traffic, where autonomous vehicles (AVs) and human-driven vehicles (HDVs) coexist. While much of the existing research on lane management focuses on highway scenarios, the complexities of managing mixed-autonomy traffic at intersections, where both lane configuration and signal timing play crucial roles, remain underexplored. This study integrates the management of dedicated AV lanes and signal optimization at isolated intersections using an analytical approach. First, we estimate the saturation flow rate in mixed lanes across varying AV penetration rates, based on the expected headway of the mixed traffic flow. Then, we analyze vehicle delay at the intersection, with lane configuration plans and signal timing as key variables, while also accounting for the assignment of AV flow between mixed and dedicated AV lanes. Building on this analytical model, we formulate a joint optimization problem for lane configuration and signal timing as a mixed-integer nonlinear programming (MINLP) model. To address the non-convex nature of the model, we decompose it into sub-problems, each informed by theoretical insights, thereby reducing solution complexity. A heuristic algorithm is then developed to solve the joint optimization problem effectively. Numerical experiments validate the superiority of the proposed joint optimization approach. Sensitivity analysis is conducted to assess the impact of various parameters, including traffic state variables and hyper-parameters for the heuristic algorithm. Furthermore, we explore scenarios in which dedicated AV lanes provide positive effects. Theoretical and numerical results offer valuable insights for improving traffic management at intersections in mixed-autonomy environments.