We study the derivation of macroscopic traffic models from car-following vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic description. We consider the superposition of Follow-the-Leader (FTL) interactions and relaxation towards a traffic-dependent Optimal Velocity (OV) and we show that the resulting macroscopic models depend on the relative frequency between these two microscopic processes. If FTL interactions dominate then one gets an inhomogeneous Aw–Rascle–Zhang model, whose (pseudo) pressure and stability of the uniform flow are precisely defined by some features of the microscopic FTL and OV dynamics. Conversely, if the rate of OV relaxation is comparable to that of FTL interactions then one gets a Lighthill–Whitham–Richards model ruled only by the OV function. We further confirm these findings by means of numerical simulations of the particle system and the macroscopic models. Unlike other formally analogous results, our approach builds the macroscopic models as physical limits of particle dynamics rather than assessing the convergence of microscopic to macroscopic solutions under suitable numerical discretisations.

我们通过 Enskog 型动力学描述的流体动力学极限研究了从跟车车辆动力学中推导出宏观交通模型。我们考虑了跟随领导者 (FTL) 交互和松弛对依赖于交通的最佳速度 (OV) 的叠加，我们表明由此产生的宏观模型取决于这两个微观过程之间的相对频率。如果 FTL 相互作用占主导地位，那么就会得到一个不均匀的 Aw-Rascle-Zhang 模型，其（伪）压力和均匀流的稳定性由微观 FTL 和 OV 动力学的某些特征精确定义。相反，如果 OV 松弛的速率与 FTL 相互作用的速率相当，那么人们就会得到一个仅由 OV 函数支配的 Lighthill-Whitham-Richards 模型。我们通过粒子系统和宏观模型的数值模拟进一步证实了这些发现。与其他形式上的类似结果不同，我们的方法将宏观模型构建为粒子动力学的物理极限，而不是在合适的数值离散化下评估微观到宏观解的收敛性。