Traffic assignment models. Numerical aspects

TL;DR

This paper discusses advanced traffic assignment models, including BMW and Nesterov-de Palma, and introduces numerical methods like universal gradient and Sinkhorn's algorithm to solve equilibrium problems efficiently.

Contribution

It presents a novel combination of optimization techniques to solve multi-stage traffic assignment equilibrium models based on entropy and saddle-point formulations.

Findings

Successful application of Sinkhorn's algorithm for traffic demand matrices

Development of a convex-concave saddle-point problem framework

Enhanced numerical methods for multi-stage traffic assignment

Abstract

In this book we describe BMW traffic assignment model and Nesterov-dePalma model. We consider Entropy model for demand matrix. Based on this models we build multi-stage traffic assignment models. The equilibrium in such models can be found from convex-concave saddle-point problem. We show how to solve this problem by using special combination of universal gradient method and Sinkhorn's algorithm.