Static Traffic Assignment Problem. A comparison between Beckmann (1956) and Nesterov & de Palma (1998) models

Since 1956, the Beckmann model is the reference for the static trafc equilibrium problem not only from a theoretical but also from a practical point of view. In 1998, Nesterov & de Palma developed a new model for the static trafc equilibrium problem. In contrast to the Beckmann model, the travel time on an arc is a variable of an optimization problem and it is not determined only by the ow on this arc. Additionally, road capacity constraints are explicitly modeled. The main objective of this work is to provide clarity on model differences both theoretically and practically. First, we consider qualitative differences between both models. In particular, the notion of delays, congestion, the detection of Braess arcs, and the price of anarchy are presented. Secondly, we study quantitative differences in the solutions of both models using large-scale benchmark instances as well as real data. For the Beckmann model, we solve the corresponding optimization problem using the VISUM software. For the Nesterov & de Palma model, we design algorithms based on non-smooth methods developed by Nesterov in 2005.