Hybrid model predictive control based dynamic pricing of managed lanes with multiple accesses

We propose a hybrid model predictive control (MPC) based dynamic tolling strategy for high-occupancy toll (HOT) lanes with multiple accesses. This approach preplans and coordinates the prices for different OD pairs and enables adaptive utilization of HOT lanes by considering available demand information and boundary conditions. It also addresses such practical issues as prevention of recurrent congestion in HOT lanes, ensuring no higher toll for a closer toll exit and fairness among different OD groups at each toll entry, as well as the fact that high occupancy vehicles (HOVs) have free access to the HOT lanes. Taking the inflows at each toll entry as the control, traffic densities and vehicle queue length as observed system states, and boundary traffic as predicted exogenous input, we formulate a discrete-time piecewise affine traffic model. Optimal tolls are then derived from a one-to-one mapping based on the optimal toll entry flows. By properly formulating the constraints, we show that the MPC problem at each stage is a mixed-integer linear program and admits an explicit control law derived by multi-parametric programing techniques. A numerical experiment is presented for a representative freeway segment to validate the effectiveness of the proposed approach. The results show that our control model can react to demand and boundary condition changes by adjusting and coordinating tolls smoothly at adjacent toll entries and drive the system to a new equilibrium that minimizes the total person delay. Under the optimal prediction horizon, the on-line computational cost of the proposed control model is only about 4% and 8% of the modeling cycle of 30 s, respectively, for two typical traffic scenarios, which implies a potential of real-time implementation.