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

Duong Viet Thong, Aviv Gibali, Mathias Staudigl*, Phan Tu Vuong

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Web of Science)

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.

Original languageEnglish
Pages (from-to)735-768
Number of pages34
JournalNetworks & Spatial Economics
Volume21
Issue number3
Early online date14 Jul 2021
DOIs
Publication statusPublished - Sep 2021

Keywords

  • Dynamic Traffic Assignment
  • Fixed Point Iteration
  • Strong Convergence
  • TRAFFIC ASSIGNMENT
  • SIMULTANEOUS ROUTE
  • EXISTENCE
  • FORMULATION
  • CONVERGENCE
  • MODEL
  • ALGORITHMS
  • OPERATOR
  • WAVES

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