Solving a Dynamic Traffic Assignment model with implicit path enumeration using Gradient Projection algorithms

This article shows how Gradient Projection (GP) algorithms are capable of solving with high precision a Dynamic Traffic Assignment (DTA) model based on implicit path enumeration. Dynamic User Equilibrium (DUE) is formulated as a Variational Inequality problem defined on temporal profiles of arc conditional probabilities, that express a sequence of deterministic route choices taken at nodes by users directed toward each destination. This model, which is fully link based, is proved to be equivalent to a path based formulation. It also allows for the computation of a handy gap function for analysing convergence to equilibrium. Congestion is represented through a macroscopic traffic model capable to reproduce a range of phenomena having increasing complexity, from links with bottleneck to intersections with spillback. Different time discretizations, from few seconds to few minutes, are also possible, which allows a range of applications from planning to operation. Numerical experiments on test networks are presented, showing that the proposed GP algorithms converge to dynamic equilibrium in a reasonable number of iterations, outperforming the Method of Successive Averages (MSA).