This paper proposes a new dynamic user equilibrium (DUE) traffic assignment model using reservoir-based network reduction techniques and surrogate dynamic network loading models. A traffic network is decomposed into a reservoir structure, and the DUE problem is formulated as a variational inequality, with an embedded surrogate model for the path delay operator to describe traffic dynamics at the reservoir level. The surrogate model is further enhanced by the reproducing kernel Hilbert space and adaptive sampling to reduce approximation error and improve computational efficiency. To solve the proposed surrogate-based DUE problem on reduced networks, we develop a customized algorithm that integrates the kernel trick with the generalized projection framework. A pre-computation scheme is proposed, which calculates and stores the of kernel matrices and vectors, could further reduce the computational burden. Numerical experiments of the proposed methods show significant reduction of the computational times, by up to $90\%$, while maintaining low approximation errors (MAPE below $6\%$), when compared to the exact models and solution methods.

本文提出了一种新的动态用户均衡（DUE）流量分配模型，该模型使用基于库的网络缩减技术和替代动态网络负载模型。交通网络被分解成一个水库结构，DUE问题被表述为一个变分不等式，并为路径延迟算子提供了嵌入式替代模型来描述水库一级的交通动态。通过重现内核Hilbert空间和自适应采样，可以进一步替代模型，以减少近似误差并提高计算效率。为了解决简化网络上建议的基于代理的DUE问题，我们开发了一种定制的算法，该算法将内核技巧与广义投影框架集成在一起。提出了预计算方案，计算和存储核矩阵和向量的向量可以进一步减轻计算负担。所提出方法的数值实验表明，计算时间显着减少了$90％$，同时保持较低的近似误差（以下为MAPE $6％$），并与确切的模型和求解方法进行比较。