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 https://github.com/DrKeHan/DTA.

中文翻译：

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通过软件实现在大型网络上计算动态用户平衡

动态用户平衡（DUE）是动态交通分配（DTA）的研究最为广泛的形式，其中，路途旅行者参与了一种非合作的，类似于Nash的具有出发时间和路线选择的游戏。DUE模型描述和预测与流量理论和旅行行为一致的网络上随时间变化的流量。本文通过介绍DUE的整体计算理论（在MATLAB软件包中以数值方式实现），记录了在综合交通流理论和DUE建模方面的理论和数值进展。尤其是，基于Lighthill-Whitham-Richards流体动力学模型，动态网络负载（DNL）子问题被公式化为微分代数方程组，该模型捕获了物理队列的形成，传播和消散以及车辆溢出在网络上。然后，采用定点算法在多个大型网络上同时选择路线和出发时间来解决DUE问题。我们公开提供MATLAB软件包，该软件包可用于解决用户定义网络上的DUE问题，不仅旨在促进对各种DUE算法和解决方案进行基准测试，而且还为研究人员提供了一个进一步开发自己的模型和平台的平台。应用程序。可从https://github.com/DrKeHan/DTA获得MATLAB软件包和计算示例。其目的不仅是促进对各种DUE算法和解决方案进行基准测试，而且还为研究人员提供了一个进一步开发自己的模型和应用程序的平台。可从https://github.com/DrKeHan/DTA获得MATLAB软件包和计算示例。其目的不仅是促进对各种DUE算法和解决方案进行基准测试，而且还为研究人员提供了一个进一步开发自己的模型和应用程序的平台。可从https://github.com/DrKeHan/DTA获得MATLAB软件包和计算示例。