从具有反应时间的交通和行人跟随-领先模型到一阶对流-扩散流模型
From traffic and pedestrian follow-the-leader models with reaction time to first order convection-diffusion flow models
AI总结：
本文从微观的延迟跟随-领先模型推导出一阶连续交通流模型，适用于车辆和行人交通流。通过最优速度函数和反应时间参数得到宏观方程，展示了模型的稳定性及数值模拟结果。
摘要：
本文从微观的延迟跟随-领先模型推导出一阶连续交通流模型，适用于车辆和行人交通流。微观模型基于最优速度函数和反应时间参数。相应的宏观方程在欧拉或拉格朗日坐标下得到一阶对流-扩散方程。对流由最优速度描述，扩散项依赖于反应时间。提供了连续和离散模型的线性稳定性分析。条件与特定空间离散化下的跟车模型一致。通过数值模拟展示了新模型的行为。当反应时间足够大时，会得到无碰撞的自维持启停动态。结果表明微观模型的动力学可由宏观方程良好捕捉。对于非零反应时间，观察到散射的基本图。散射宽度与真实行人和道路交通数据进行比较。
英文摘要：
In this work, we derive first order continuum traffic flow models from a microscopic delayed follow-the-leader model. Those are applicable in the context of vehicular traffic flow as well as pedestrian traffic flow. The microscopic model is based on an optimal velocity function and a reaction time parameter. The corresponding macroscopic formulations in Eulerian or Lagrangian coordinates result in first order convection-diffusion equations. More precisely, the convection is described by the optimal velocity while the diffusion term depends on the reaction time. A linear stability analysis for homogeneous solutions of both continuous and discrete models are provided. The conditions match the ones of the car-following model for specific values of the space discretization. The behavior of the novel model is illustrated thanks to numerical simulations. Transitions to collision-free self-sustained stop-and-go dynamics are obtained if the reaction time is sufficiently large. The results show that the dynamics of the microscopic model can be well captured by the macroscopic equations. For non--zero reaction times we observe a scattered fundamental diagram. The scattering width is compared to real pedestrian and road traffic data.
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