Convexification approaches for regional route guidance and demand management with generalized MFDs

Traffic congestion is one of the main concerns in big cities with many adverse socioeconomic effects. A promising solution is to simultaneously regulate the admission of vehicles (i.e., demand management) and redistribute traffic flows within the network (i.e., route guidance). In this work, we integrate demand management with route guidance within a Model Predictive Control framework using regional traffic dynamics with generalized Macroscopic Fundamental Diagram (MFD) shapes. Dealing with generalized MFD shapes is challenging due to the resulting nonlinear and non-convex optimization formulation. To tackle this challenge, we develop two real-time solution approaches: (i) a successive convexification approach that constructs convex bounding sets for all nonlinear terms, and (ii) a linear approximation approach that solves the problem using triangular macroscopic fundamental diagram approximations. The proposed approaches offer a trade-off between execution speed and solution quality, as the linear approximation approach runs faster while the successive convexification approach yields better quality and accuracy solutions. Macroscopic simulation results illustrate the efficiency of the successive convexification and linear approximation approaches yielding an optimality gap of less than 3.5% and 10% in all considered cases, respectively. Furthermore, both approaches outperform a state-of-practice nonlinear solver in terms of solution quality and execution time. Finally, substantial gains are also obtained regarding travel time and traffic flow efficiency in a realistic microsimulation environment.