Computational Efficiency Analysis of Macroscopic Fundamental Diagram-Based Optimal Road Traffic Flow Control Methods

Traffic modeling and control in large-scale urban road networks present significant challenges. The macroscopic fundamental diagram provides a means of formulating dynamical traffic models of such networks, thereby enabling the development of model-based design techniques for state estimation and feedback control. In this article we focus on the computational efficiency of macroscopic fundamental diagram-based nonlinear model predictive control schemes for perimeter control and route guidance actuated networks, which are macroscopic actuation methods involving traffic flow manipulation between adjacent network neighborhoods. A number of economic nonlinear model predictive control schemes, based on direct methods from the numerical optimal control literature, are implemented using a variety of nonlinear programming solvers. The computational efficiency of the schemes is evaluated via computer simulations of congestion control scenarios for macroscopic fundamental diagram-based network models with different numbers of regions using randomly generated traffic demand profiles. The results indicate that the proper pairing of direct methods and solvers yields significant improvements in computational efficiency for macroscopic fundamental diagram-based control schemes, thereby improving the real-time feasibility and, consequently, the field deployment potential of the resulting macroscopic road traffic flow control algorithms.