Computing Dynamic User Equilibria on Large-Scale Networks: From Theory to Software Implementation

TL;DR

This paper advances the computational modeling of dynamic user equilibrium (DUE) in large-scale networks by integrating traffic flow theory with a MATLAB software package for solving DUE problems efficiently.

Contribution

It presents a holistic computational framework for DUE, including a differential algebraic equations-based dynamic network loading model and a fixed-point algorithm, with an open-source MATLAB implementation.

Findings

Effective solution of DUE on large networks using fixed-point algorithm.

Open-source MATLAB package facilitates benchmarking and further research.

Model captures queue formation, propagation, and spillback phenomena.

Abstract

Dynamic user equilibrium (DUE) is the most widely studied form of dynamic traffic assignment, in which road travelers engage in a non-cooperative Nash-like game with departure time and route choices. DUE models describe and predict the time-varying traffic flows on a network consistent with traffic flow theory and travel behavior. This paper documents theoretical and numerical advances in synthesizing traffic flow theory and DUE modeling, by presenting a holistic computational theory of DUE with numerical implementation encapsulated in a MATLAB software package. In particular, the dynamic network loading (DNL) sub-problem is formulated as a system of differential algebraic equations based on the fluid dynamic model, which captures the formation, propagation and dissipation of physical queues as well as vehicle spillback on networks. Then, the fixed-point algorithm is employed to solve the DUE problems on several large-scale networks. We make openly available the MATLAB package, which can be used to solve DUE problems on user-defined networks, aiming to not only help DTA modelers with benchmarking a wide range of DUE algorithms and solutions, but also offer researchers a platform to further develop their own models and applications. Updates of the package and computational examples are available at https://github.com/DrKeHan/DTA.