Road traffic conditions exhibit spatial and temporal variations influenced by factors such as construction, speed limits, and accidents. Accurate and efficient modeling of vehicular flow on changing road conditions is crucial for understanding intricate traffic phenomena and analyzing dynamic characteristics in real-world scenarios. In this paper, we develop a rapid numerical approach that computes traffic flow solutions for roads divided into multiple sections with varying traffic conditions, utilizing the Lighthill-Whitham-Richards model as the mathematical framework. The key aspect of our approach lies in solving the flow at the dividing point between consecutive road sections with different traffic conditions. For the two-section road scenario, we integrate the Hamilton-Jacobi formulation of the traffic model with the triangular fundamental diagram, capturing the explicit relationship between flow and density. This integration allows us to derive the spatiotemporal solution for a single dividing point. By accounting for the dynamic interaction between adjacent dividing points, we extend the applicability of our approach to an arbitrary number of road sections based on a semi-analytic Lax-Hopf formula. Our semi-analytical method is distinguished by grid-free computing, reducing computational demands and ensuring exceptional simulation speed. Particularly noteworthy is the formulation's remarkable efficacy in handling the complexities of heterogeneous road traffic conditions, marked by dynamic variations in both time and space, surpassing traditional macroscopic traffic flow simulations. To demonstrate its effectiveness, we apply the proposed approach to an optimization example involving traffic signal timing in a complex road environment. Additionally, we showcase its predictive capabilities by efficiently evaluating the impact of traffic accidents on the surrounding traffic flow. This research provides valuable insights for traffic management, optimization, and decision-making, enabling the analysis of complex scenarios and facilitating the development of strategies to enhance traffic efficiency and safety.

中文翻译：

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道路条件变化时交通流建模的快速半解析方法及其应用


道路交通状况表现出受施工、速度限制和事故等因素影响的空间和时间变化。在不断变化的道路条件下准确有效地建模车流对于理解复杂的交通现象和分析现实场景中的动态特征至关重要。在本文中，我们开发了一种快速数值方法，利用 Lighthill-Whitham-Richards 模型作为数学框架，计算分为具有不同交通条件的多个路段的道路的交通流解决方案。我们方法的关键在于解决不同交通条件下连续路段之间分界点的流量。对于两段道路场景，我们将交通模型的 Hamilton-Jacobi 公式与三角基本图相结合，捕捉流量和密度之间的明确关系。这种积分使我们能够导出单个分割点的时空解。通过考虑相邻划分点之间的动态相互作用，我们基于半解析 Lax-Hopf 公式将我们的方法的适用性扩展到任意数量的路段。我们的半解析方法的特点是无网格计算，减少了计算需求并确保了卓越的模拟速度。特别值得注意的是，该公式在处理复杂的异构道路交通条件（以时间和空间的动态变化为特征）方面具有显着的功效，超越了传统的宏观交通流模拟。为了证明其有效性，我们将所提出的方法应用于涉及复杂道路环境中交通信号配时的优化示例。 此外，我们通过有效评估交通事故对周围交通流量的影响来展示其预测能力。这项研究为交通管理、优化和决策提供了宝贵的见解，能够分析复杂的场景并促进制定提高交通效率和安全的策略。