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Dynamic user equilibrium (DUE) is the most widely studied form of dynamictraffic assignment, in which road travelers engage in a non-cooperativeNash-like game with departure time and route choices. DUE models describe andpredict the time-varying traffic flows on a network consistent with trafficflow theory and travel behavior. This paper documents theoretical and numericaladvances in synthesizing traffic flow theory and DUE modeling, by presenting aholistic computational theory of DUE with numerical implementation encapsulatedin a MATLAB software package. In particular, the dynamic network loading (DNL)sub-problem is formulated as a system of differential algebraic equations basedon the fluid dynamic model, which captures the formation, propagation anddissipation of physical queues as well as vehicle spillback on networks. Then,the fixed-point algorithm is employed to solve the DUE problems on severallarge-scale networks. We make openly available the MATLAB package, which can beused to solve DUE problems on user-defined networks, aiming to not only helpDTA modelers with benchmarking a wide range of DUE algorithms and solutions,but also offer researchers a platform to further develop their own models andapplications. Updates of the package and computational examples are availableat https://github.com/DrKeHan/DTA.

Computing Dynamic User Equilibria on Large-Scale Networks: From Theory to Software Implementation