Sags and tunnels are major bottlenecks, where the road capacity is reduced, and the “capacity drop” phenomenon occurs; however, there is no simple model or theory that can explain the formation and other characteristics of capacity drop. This paper presents a car-following model, which is equivalent to a continuum model in the Lagrangian coordinates. The model is built on two main assumptions: (i) inhomogeneous fundamental diagrams with location-dependent time gaps, and (ii) bounded acceleration. We first demonstrate that the stationary speed profiles, the low acceleration rates, the dropped capacity, and the approximate time duration of the capacity drop formation in the model are consistent with empirical observations. Then the impacts on the stationary states and dropped capacity of the numerical viscosity caused by the discretization method are investigated, and it is shown that the dropped capacity converges to the theoretical value. Further, a one-dimensional iterated function system is proposed to model the formation mechanism of the capacity drop, which is derived by investigating the spatial pattern of equilibrium and bounded acceleration traffic states that arises in a lead-vehicle problem. Utilizing this model, we uncover a set of properties of the capacity drop such as existence, uniqueness, global convergence, and convergence speed. Finally, the model is applied to analyze the impacts of heterogeneous drivers. The model and insights in this study will help to develop control and management schemes to alleviate capacity drop effects with connected and autonomous vehicles in the future.

凹陷和隧道是主要瓶颈，道路通行能力下降，并出现“通行能力下降”现象；但是，没有简单的模型或理论可以解释能力下降的形成和其他特征。本文提出了一个跟车模型，它等效于拉格朗日坐标系中的连续模型。该模型基于两个主要假设：（i）具有随位置而定的时间间隙的不均匀基础图，以及（ii）有界加速度。我们首先证明模型中的平稳速度曲线，低加速度，下降的容量以及容量下降形成的大致持续时间与经验观察一致。然后研究了离散化方法对数值粘度对稳态和下降容量的影响，结果表明下降容量收敛于理论值。此外，提出了一种一维迭代函数系统，以对容量下降的形成机理进行建模，该能力下降是通过研究在铅车问题中出现的平衡和有界加速交通状态的空间模式得出的。利用该模型，我们发现了容量下降的一组属性，例如存在性，唯一性，全局收敛性和收敛速度。最后，将模型应用于分析异构驱动程序的影响。