论文标题
对车辆交通的非本地动力学描述的宏观限制
Macroscopic limits of non-local kinetic descriptions of vehicular traffic
论文作者
论文摘要
我们将宏观交通模型的推导以最佳的速度和遵循领先的粒子动力学作为非本地Povzner型动力学方程的流体动力学限制。作为第一步，我们表明最佳速度车辆动力学产生了具有非本地通量的一阶宏观模型。接下来，我们表明，至少在相互作用的非本地性非常小时，非本地遵循领导的车辆动力学在第二阶AW-Rascle-zhang交通模型中具有通用的宏观对应物。最后，我们表明，基于车辆的进展而不是速度，同样的定性结果也适用于一般的跟随领导动态类别。我们还通过数值模拟研究了粒子模型的溶液及其宏观极限之间的对应关系。
We study the derivation of macroscopic traffic models out of optimal speed and follow-the-leader particle dynamics as hydrodynamic limits of non-local Povzner-type kinetic equations. As a first step, we show that optimal speed vehicle dynamics produce a first order macroscopic model with non-local flux. Next, we show that non-local follow-the-leader vehicle dynamics have a universal macroscopic counterpart in the second order Aw-Rascle-Zhang traffic model, at least when the non-locality of the interactions is sufficiently small. Finally, we show that the same qualitative result holds also for a general class of follow-the-leader dynamics based on the headway of the vehicles rather than on their speed. We also investigate the correspondence between the solutions to particle models and their macroscopic limits by means of numerical simulations.
