A finite element approach for the traffic assignment problem

Abstract

In this article, a reduced order model for the Transportation Assignment Problem (TAP), based on a Finite Element Approach (FEA), is proposed. Such methodology involves four main ideas: a) the TAP formulation including, as variables, the travel times from any node of the network to the corresponding destination points; b) the solution of the governing algebraic equation system by means of an efficient iterative approach, known as “Physarum”, that takes the travel times as the main unknowns; c) the interpolation of travel times in certain urban subdomains, denominated “finite elements”, in terms of the values corresponding to some main nodes previously selected (reduced unknowns); d) the use of the Galerkin’s method to express the TAP in terms of the reduced unknowns. The model formulation is presented and a numerical example is given to show its efficiency.