Dynamic user equilibrium (DUE) is a Nash-like solution concept describing an equilibrium in dynamic traffic systems over a fixed planning period. DUE is a challenging class of equilibrium problems, connecting network loading models and notions of system equilibrium in one concise mathematical framework. Recently, Friesz and Han introduced an integrated framework for DUE computation on large-scale networks, featuring a basic fixed-point algorithm for the effective computation of DUE. In the same work, they present an open-source MATLAB toolbox which allows researchers to test and validate new numerical solvers. This paper builds on this seminal contribution, and extends it in several important ways. At a conceptual level, we provide new strongly convergent algorithms designed to compute a DUE directly in the infinite-dimensional space of path flows. An important feature of our algorithms is that they give provable convergence guarantees without knowledge of global parameters. In fact, the algorithms we propose are adaptive, in the sense that they do not need a priori knowledge of global parameters of the delay operator, and which are provable convergent even for delay operators which are non-monotone. We implement our numerical schemes on standard test instances, and compare them with the numerical solution strategy employed by Friesz and Han.

动态用户均衡 (DUE) 是一种类似纳什的解决方案概念，用于描述固定规划周期内动态交通系统中的均衡。DUE 是一类具有挑战性的均衡问题，它将网络负载模型和系统均衡概念连接在一个简洁的数学框架中。最近，Friesz 和 Han 介绍了一种用于大规模网络上 DUE 计算的集成框架，该框架具有用于有效计算 DUE 的基本定点算法。在同一项工作中，他们提出了一个开源 MATLAB 工具箱，允许研究人员测试和验证新的数值求解器。本文建立在这一开创性贡献的基础上，并在几个重要方面对其进行了扩展。在概念层面，我们提供了新的强收敛算法，旨在直接在路径流的无限维空间中计算 DUE。我们算法的一个重要特征是它们在不了解全局参数的情况下提供可证明的收敛保证。事实上，我们提出的算法是自适应的，因为它们不需要延迟算子的全局参数的先验知识，并且即使对于非单调的延迟算子也可证明收敛。我们在标准测试实例上实施我们的数值方案，并将它们与 Friesz 和 Han 采用的数值求解策略进行比较。并且即使对于非单调的延迟算子也可证明收敛。我们在标准测试实例上实施我们的数值方案，并将它们与 Friesz 和 Han 采用的数值求解策略进行比较。并且即使对于非单调的延迟算子也可证明收敛。我们在标准测试实例上实施我们的数值方案，并将它们与 Friesz 和 Han 采用的数值求解策略进行比较。