  Dynamic user equilibrium (DUE) is the most widely studied form of dynamic
traffic assignment, 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 with numerical implementation encapsulated
in a MATLAB software package. In particular, the dynamic network loading (DNL)
sub-problem is formulated as a system of differential algebraic equations based
on the 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 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 help
DTA modelers with benchmarking a wide range of DUE algorithms and solutions,
but also offer researchers a platform to further develop their own models and
applications. Updates of the package and computational examples are available
at https://github.com/DrKeHan/DTA.
