This paper addresses the first-order extension of the Lighthill–Whitham– Richards (LWR) macroscopic traffic flow model. Although previous studies have focused on the fluid aspect of traffic flow, none have addressed the sensitivity of drivers to the number of free spaces within a certain distance ahead of the subject driver. To incorporate driver behavior, we used the number of free spaces ahead of subject drivers and their sensitivity to the number of free spaces within a certain distance ahead. The resulting model is a convection-diffusion model. By computing Einstein's diffusion equation and comparing it with the diffusion coefficient in the extended model, a theoretical relation for the driver's sensitivity was derived. A representation of the numerical results of the LWR model, the convection-diffusion model with a typical diffusion coefficient, and the extended model showed that the proposed model has a lower mean relative error value.

中文翻译：

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一个宏观交通流模型，包括驾驶员对前方可用空间数量的敏感性

本文讨论了 Lighthill-Whitham-Richards (LWR) 宏观交通流模型的一阶扩展。尽管以前的研究集中在交通流的流动方面，但没有一项研究解决了驾驶员对目标驾驶员前方一定距离内可用空间数量的敏感性。为了结合驾驶员行为，我们使用了主题驾驶员前方的可用空间数量及其对前方特定距离内可用空间数量的敏感性。得到的模型是对流扩散模型。通过计算爱因斯坦的扩散方程并将其与扩展模型中的扩散系数进行比较，推导出驾驶员灵敏度的理论关系。LWR 模型数值结果的表示，