Model Predictive Control of a Freeway Network with Capacity Drops

In this paper, we present a model predictive controller to reduce road traffic congestion in freeway networks. The model predictive controller regulates traffic in the freeway through the use of ramp metering and variable speed limits. The controller uses a Link-Node Cell transmission model (LN-CTM) to represent freeway dynamics. We modify the standard LN-CTM to account for the capacity drop phenomenon, which is observed as a discontinuous decrease in flow throughput when traffic density exceeds a critical value. The resulting optimal control problem with a modified model, which accounts for the capacity flow phenomenon, is non-convex. We present heuristic restrictions on the solution trajectories, which allow us to solve the problem efficiently. This enables us to obtain the solution of the actual optimal control problem by solving a sequence of relaxed linear programs. We describe the procedure which can be used to map the optimal solution of this relaxed problem to the solution of the actual optimal control problem. Finally, we demonstrate the application of the model predictive controller on a simulated example, and discuss the characteristics of the controller.