Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation

Ke Han, Gabriel Eve, Terry L. Friesz

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


Dynamic user equilibrium (DUE) is the most widely studied form of dynamic traffic assignment (DTA), 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, which is numerically implemented in a MATLAB package. In particular, the dynamic network loading (DNL) sub-problem is formulated as a system of differential algebraic equations based on the Lighthill-Whitham-Richards 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 with simultaneous route and departure time choices 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 facilitate benchmarking a wide range of DUE algorithms and solutions, but also offer researchers a platform to further develop their own models and applications. The MATLAB package and computational examples are available at

Original languageEnglish (US)
Pages (from-to)869-902
Number of pages34
JournalNetworks and Spatial Economics
Issue number3
StatePublished - Sep 15 2019

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Networks and Communications
  • Artificial Intelligence


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