A finite element approach for the traffic assignment problem

Abstract

Traffic assignment problem (TAP) in static equilibrium conditions is based on the Wardrop´s first principle. The mathematical solution of this problem involves significant computation times for the analysis of large transportation networks, especially in the context of design. Thus, the development of efficient computational methodologies is of the greatest concern. In this article, a reduced order model for 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.