Computing Dynamic User Equilibrium on Large-Scale Networks Without Knowing Global Parameters

TL;DR

This paper introduces adaptive algorithms for computing dynamic user equilibrium in large-scale traffic networks that do not require prior knowledge of global parameters, ensuring convergence even with complex delay operators.

Contribution

It develops strongly convergent, adaptive algorithms for DUE computation that operate without global parameter knowledge, extending previous fixed-point methods.

Findings

Algorithms are provably convergent without global parameters.

Numerical schemes outperform existing methods on standard tests.

Effective in handling non-monotone delay operators.

Abstract

Dynamic user equilibrium (DUE) is a Nash-like solution concept describing an equilibrium in dynamic traffic systems over a fixed planning period. DUE is a challenging class of equilibrium problems, connecting network loading models and notions of system equilibrium in one concise mathematical framework. Recently, Friesz and Han introduced an integrated framework for DUE computation on large-scale networks, featuring a basic fixed-point algorithm for the effective computation of DUE. In the same work, they present an open-source MATLAB toolbox which allows researchers to test and validate new numerical solvers. This paper builds on this seminal contribution, and extends it in several important ways. At a conceptual level, we provide new strongly convergent algorithms designed to compute a DUE directly in the infinite-dimensional space of path flows. An important feature of our algorithms is that they give provable convergence guarantees without knowledge of global parameters. In fact, the algorithms we propose are adaptive, in the sense that they do not need a priori knowledge of global parameters of the delay operator, and which are provable convergent even for delay operators which are non-monotone. We implement our numerical schemes on standard test instances, and compare them with the numerical solution strategy employed by Friesz and Han.