标题： 容量下降的运动波理论 显示英文标题

标题： A kinematic wave theory of capacity drop

摘要： 在活跃瓶颈处的容量下降是交通现象中最令人困惑的一种，但对其深入理解对于设计可变速度限制和匝道计量策略具有实际重要性。 在本研究中，我们尝试在运动波理论框架内开发一个简单的容量下降模型，该模型基于这样一个观察结果：当在活跃瓶颈处形成上游队列时会发生容量下降。 此外，我们假设稳态下的基本图是连续的。 这一假设与观察结果一致，并可以避免不连续基本图中的不现实的无限特征波速。 新模型的核心是一个由不连续边界通量函数定义的熵条件。 对于车道减少区域，我们证明了该模型是定义良好的，其黎曼问题可以被唯一求解。 我们理论讨论了在密度、上游需求和下游供应扰动下该模型的交通稳定性。 我们澄清了不连续的流量-密度关系，或所谓的“不连续”基本图，是由于对交通状态的不完整观测造成的。 理论结果与文献中的观察结果一致，并通过数值模拟和实证观测得到了验证。 最后，我们讨论了潜在的应用和未来的研究方向。 显示英文摘要

摘要： Capacity drop at active bottlenecks is one of the most puzzling traffic phenomena, but a thorough understanding is practically important for designing variable speed limit and ramp metering strategies. In this study, we attempt to develop a simple model of capacity drop within the framework of kinematic wave theory based on the observation that capacity drop occurs when an upstream queue forms at an active bottleneck. In addition, we assume that the fundamental diagrams are continuous in steady states. This assumption is consistent with observations and can avoid unrealistic infinite characteristic wave speeds in discontinuous fundamental diagrams. A core component of the new model is an entropy condition defined by a discontinuous boundary flux function. For a lane-drop area, we demonstrate that the model is well-defined, and its Riemann problem can be uniquely solved. We theoretically discuss traffic stability with this model subject to perturbations in density, upstream demand, and downstream supply. We clarify that discontinuous flow-density relations, or so-called "discontinuous" fundamental diagrams, are caused by incomplete observations of traffic states. Theoretical results are consistent with observations in the literature and are verified by numerical simulations and empirical observations. We finally discuss potential applications and future studies.