Optimizing Urban Traffic Networks With Dynamic Saturation Rates in a Mixed Autonomy Environment

This work presents a novel optimization-based control framework for managing traffic flow in urban networks with mixed autonomy, where Connected and Automated Vehicles (CAVs) and Human-Driven Vehicles (HDVs) coexist. The proposed approach extends the store-and-forward model by incorporating a dynamic saturation flow rate that reflects the level of autonomy in vehicle queues. The problem is formulated as a Non-convex Quadratic Program (NQP), capturing the dynamics of queue lengths, spillback effects, green time allocation, CAV routing, and variable saturation flow rates. To solve the NQP efficiently, we reformulate bilinear terms using under- and over estimators, transforming the non-convex problem into a series of convex subproblems—specifically, a Mixed-Integer Quadratic Program (MIQP)—which is further converted into a Mixed-Integer Linear Program (MILP) by linearizing quadratic terms in the objective function. This approach significantly reduces computational complexity while enabling potential real-time implementation. Numerical simulations on a grid network demonstrate the effectiveness and efficiency of the proposed methodology.