Resolving freeway jam waves by discrete first-order model-based predictive control of variable speed limits

In this paper we develop a fast model predictive control (MPC) approach for variable speed limit coordination to resolve freeway jam waves. Existing MPC approaches that are based on the second-order traffic flow models suffer from high computation load due to the non-linear and non-convex optimization formulation. In recent years, simplified MPC approaches which are based on discrete first-order traffic flow models have attracted more and more attention because they are beneficial for real-time applications. In literature, the type of traffic jam resolved by these approaches is limited to the standing queue in which the jam head is fixed at the bottleneck. Another type of traffic jam known as the jam wave, has been neglected by the discrete first-order model-based MPC approaches. To fill this gap, we develop a fast MPC approach based on a more accurate discrete first-order model. The model keeps the linear property of the classical discrete first-order model, meanwhile takes traffic flow features of jam waves propagation into consideration. A classical non-linear MPC and a recently proposed linear MPC are compared with the proposed MPC in terms of computation speed and jam wave resolution by a benchmark problem. Simulation results show that the proposed MPC resolves the jam wave with a real-time feasible computation speed.