Theoretical analysis demonstrates static user equilibrium is a special case of dynamic models in transportation networks, indicating dynamic equilibrium generalizes static flow.
Understanding the relationship between the static user equilibrium (SUE) problem and the dynamic user equilibrium (DUE) problem is fundamental to solving transportation network problems, such as transportation demand analysis, transportation planning and management. Though the SUE and DUE problems were studied broadly, they were studied separately in most previous studies. In this paper, first, the variational inequality (VI) models for the SUE and DUE problems are presented. Then the analysis of the relationship between the DUE and SUE is presented. The study shows that the SUE is a special case for the DUE when the assignment interval is taken as one. And the DUE problem is a dynamic generalization of the SUE problem. Our study helps better understand the SUE and DUE problems.
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Xu et al. (2026) studied this question.
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