Path marginal cost (PMC) is a crucial component in solving path-based system-optimal dynamic traffic assignment (SO-DTA), dynamic origin-destination demand estimation (DODE), and network resilience analysis. However, accurately evaluating PMC in heterogeneous traffic conditions poses significant challenges. Previous studies often focus on homogeneous traffic flow of single vehicle class and do not well address the interactive effect of heterogeneous traffic flows and the resultant computational issues. This study proposes a novel but simple method for approximately evaluating PMC in complex heterogeneous traffic condition. The method decomposes PMC into intra-class and inter-class terms and uses conversion factor derived from heterogeneous link dynamics to explicitly model the intricate relationships between vehicle classes. Additionally, the method considers the non-differentiable issue that arises when mixed traffic flow approaches system optimum conditions. The proposed method is tested on a small corridor network with synthetic demand and a large-scale network with calibrated demand from real-world data. Results demonstrated that our method exhibits superior performance in solving bi-class SO-DTA problems, yielding lower total travel cost and capturing the multi-class flow competition at the system optimum state.

翻译：路径边际成本（PMC）是解决基于路径的系统最优动态交通分配（SO-DTA）、动态起讫点需求估计（DODE）以及网络韧性分析的关键组成部分。然而，在异构交通条件下准确评估PMC面临重大挑战。先前的研究通常聚焦于单一车辆类别的同质交通流，未能很好地处理异构交通流之间的交互效应及其带来的计算问题。本研究提出了一种新颖而简单的方法，用于在复杂的异构交通条件下近似评估PMC。该方法将PMC分解为类内项与类间项，并利用源自异构路段动力学的转换因子，显式地建模不同车辆类别之间复杂的关系。此外，该方法还考虑了当混合交通流趋近系统最优条件时可能出现的不可微问题。所提出的方法在一个具有合成需求的小型走廊网络和一个基于真实数据校准需求的大规模网络上进行了测试。结果表明，我们的方法在解决双类别SO-DTA问题上表现出优越的性能，能够获得更低的总出行成本，并捕捉到系统最优状态下多类别交通流之间的竞争关系。