This paper proposes a two-dimensional car-following model to tackle traffic flow problems where considering continuum lateral distances enables a simpler or more natural mathematical formulation compared to traditional car-following models. These problems include (i) the effects of lateral friction often observed in HOV lanes and diverge bottlenecks, (ii) the relaxation phenomenon at merge bottlenecks, (iii) the occurrence of accidents due to lane changing, and (iv) traffic models for autonomous vehicles (AVs). We conjecture that traditional car-following models, where the lateral dimension is discretized into lanes, struggle with these problems and one has to resort to ad-hoc rules conceived to directly achieve the desired effect, and that are difficult to validate.

We argue that the distance maintained by drivers in order to avoid collisions in all directions plays a fundamental role in all these problems. To test this hypothesis, we propose a simple two-dimensional microscopic car-following model based on the social force paradigm, and build simulation experiments that reproduce these phenomena. These phenomena are reproduced as an indirect consequence of the model’s formulation, as opposed to ad-hoc rules, thus shedding light on their causes.

A better understanding of the behavior of human drivers in the lateral dimension can be translated to improving autonomous driving algorithms so that they are human-friendly. In addition, since AV technology is proprietary, we argue that the proposed model should provide a good starting point for building AV traffic flow models when real data becomes available, as these data come from sensors that cover two-dimensional regions.

本文提出了一种二维汽车跟随模型来解决交通流量问题，在这种模型中，考虑到连续的横向距离，与传统的汽车跟随模型相比，它可以简化或更自然的数学公式。这些问题包括（i）在HOV车道中经常观察到的横向摩擦的影响和发散瓶颈；（ii）合并瓶颈处的松弛现象；（iii）变道导致的事故发生；以及（iv）自主交通模型车辆（AV）。我们推测，传统的跟车模型将侧向尺寸离散化为车道，要解决这些问题，并且必须诉诸专门为直接实现所需效果而设计的特殊规则，而这些规则很难验证。

我们认为，驾驶员避免所有方向碰撞所保持的距离在所有这些问题中都起着根本性的作用。为了验证该假设，我们基于社会力量范式提出了一个简单的二维微观汽车跟随模型，并建立了重现这些现象的仿真实验。与临时规则相反，这些现象是模型制定的间接结果而复制，从而阐明了其原因。

可以更好地理解驾驶员在横向方向上的行为，从而可以改进自动驾驶算法，从而使它们对人类友好。此外，由于AV技术是专有技术，因此我们认为，当实际数据可用时，建议的模型应该为构建AV交通流模型提供一个良好的起点，因为这些数据来自覆盖二维区域的传感器。