M. Hajiahmadi, B. De Schutter, and H. Hellendoorn, "Model predictive traffic control: A mixed-logical dynamic approach based on the link transmission model," Proceedings of the 13th IFAC Symposium on Control in Transportation Systems (CTS'2012), Sofia, Bulgaria, pp. 144-149, Sept. 2012.
In this paper, model predictive control of traffic networks using first-order macroscopic link transmission model (LTM) is considered. The LTM model provides fast yet accurate predictions for traffic networks compared to other models. In order to use this model for traffic control, it is extended to include ramp metering. Using the extended LTM model as prediction model in a model predictive control framework, one can determine optimal control signals for metered on-ramps. However, the optimization problem is still nonlinear and nonconvex, and in general it is not tractable to find its global optimum, as global or multi-start local optimization techniques take considerable time. Therefore, in this paper the extended LTM model is transformed into a mixed logical dynamic model. The resulting optimization problem can be recast as a mixed integer linear program (MILP) that can be solved much more efficiently than the nonlinear optimization problem, and it allows to determine a global optimum efficiently. A simple case study is selected, first to test the modeling performance of the extended LTM and next to compare the control performance of the MILP approach and the original nonlinear formulation in terms of computational efficiency and total cost.