2020/10/08 by Duong Viet Thong, Aviv Gibali, Thong, Duong Viet +5 · 1 citation
Engineering · Social Sciences · #Evacuation and Crowd Dynamics #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #Traffic control and management #Transportation Planning and Optimization #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2010.04597
openalex publication_date 2020/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dynamic user equilibrium (DUE) is a Nash-like solution concept describing an\nequilibrium in dynamic traffic systems over a fixed planning period. DUE is a\nchallenging class of equilibrium problems, connecting network loading models\nand notions of system equilibrium in one concise mathematical framework.\nRecently, Friesz and Han introduced an integrated framework for DUE computation\non large-scale networks, featuring a basic fixed-point algorithm for the\neffective computation of DUE. In the same work, they present an open-source\nMATLAB toolbox which allows researchers to test and validate new numerical\nsolvers. This paper builds on this seminal contribution, and extends it in\nseveral important ways. At a conceptual level, we provide new strongly\nconvergent algorithms designed to compute a DUE directly in the\ninfinite-dimensional space of path flows. An important feature of our\nalgorithms is that they give provable convergence guarantees without knowledge\nof global parameters. In fact, the algorithms we propose are adaptive, in the\nsense that they do not need a priori knowledge of global parameters of the\ndelay operator, and which are provable convergent even for delay operators\nwhich are non-monotone. We implement our numerical schemes on standard test\ninstances, and compare them with the numerical solution strategy employed by\nFriesz and Han.\n