A MILP Framework to Solve System Optimum with Link MFD Functions

Abstract

This work aims to calculate the optimal routing strategy minimizing total travel time in a transportation network. We solve a mixed integer linear program (MILP) for the system-optimum dynamic traffic assignment with a link-based Macroscopic Fundamental Diagram (SO-MFDDTA) and with multiple origins and destinations. Previous studies resort to cell transmission model and triangular fundamental diagram to describe traffic dynamics. Here, each link is associated with a single cell characterized by a more advanced cost-function: the link-MFD better describing the speed variation related to the network loading and traffic control impacts. Link MFDs are approximated by piecewise linear functions and adapted to the MILP framework by employing the convex combination method with special ordered sets of type 2 variables. Vehicle holding (VH) that originates from the linearization of traffic model is also addressed. Finally, on a synthetic network, we present the sensitivity analysis on the parameters of the model.