Linear MPC-Based Urban Traffic Control Using the Link Transmission Model

In this paper a novel computationally efficient model predictive control (MPC) method for optimizing flows at urban intersections is proposed. Several linear and quadratic MPC approaches have been developed in the literature to reduce the computational complexity of the problem, but without considering the back-propagating waves associated with spillback. As the principal contribution of this work, a linear optimization problem for an MPC approach is formulated, which considers downstream propagating waves linked to free-flow traffic, queuing dynamics, and upstream propagating waves related to spillback (i.e. forward and backward moving waves, respectively). The linear optimization problem is obtained by describing link dynamics using the link transmission model, and aggregating the traffic dynamics to (several) tens of seconds. The performance of the proposed controller is compared with two other existing strategies; a store-and-forward model-based, and a cell transmission model-based approach. The total time spent (TTS) by all the vehicles in the network and the computation time is applied as performance indexes for the evaluation of the control strategies. Simulation results show that including upstream propagating waves results in better controller performance, due to the explicit modeling of the impact of link outflow on the maximum link inflow.