Car taillights are ubiquitous during the deceleration process in real traffic, while drivers have a memory for historical information. The collective effect may greatly affect driving behavior and traffic flow performance. In this paper, we propose a continuum model with the driver’s memory time and the preceding vehicle’s taillight. To better reflect reality, the continuous driving process is also considered. To this end, we first develop a unique version of a car-following model. By converting micro variables into macro variables with a macro conversion method, the micro car-following model is transformed into a new continuum model. Based on a linear stability analysis, the stability conditions of the new continuum model are obtained. We proceed to deduce the modified KdV-Burgers equation of the model in a nonlinear stability analysis, where the solution can be used to describe the propagation and evolution characteristics of the density wave near the neutral stability curve. ...

中文翻译：

---

具有驾驶员连续感官记忆和前车尾灯的新型连续体模型

在实际交通中，汽车尾灯在减速过程中无处不在，而驾驶员则可以存储历史信息。集体效应可能极大地影响驾驶行为和交通流性能。在本文中，我们提出了一个具有驾驶员记忆时间和前车尾灯的连续模型。为了更好地反映现实，还考虑了连续驾驶过程。为此，我们首先开发了汽车跟随模型的独特版本。通过使用宏转换方法将微变量转换为宏变量，将微型汽车跟随模型转换为新的连续模型。基于线性稳定性分析，获得了新的连续模型的稳定性条件。在非线性稳定性分析中，我们继续推导模型的修正KdV-Burgers方程，该解可以用来描述中性稳定曲线附近的密度波的传播和演化特征。...