Macroscopic traffic flow modeling is essential for describing and forecasting the characteristics of traffic flow. However, the classic Lighthill–Whitham–Richards (LWR) model only provides equilibrium values for steady-state conditions and fails to capture common stochastic variabilities, which are a necessary component of accurate modeling of real-time traffic management and control. In this paper, a stochastic LWR (SLWR) model that randomizes free-flow speed is developed to account for the stochasticity incurred by the heterogeneity of drivers, while holding individual drivers’ behavior constant. The SLWR model follows a conservation law of stochastic traffic density and flow and is formulated as a time-dependent stochastic partial differential equation. The model is solved using a dynamically bi-orthogonal (DyBO) method based on a spatial basis and stochastic basis. Various scenarios are simulated and compared with the Monte Carlo (MC) method, and the results show that the SLWR model can effectively describe dynamic traffic evolutions and reproduce some commonly observed traffic phenomena. Furthermore, the DyBO method shows significant computational advantages over the MC method.

中文翻译：

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随机Lighthill-Whitham-Richards交通流模型的动态双正交求解方法

宏观交通流建模对于描述和预测交通流特征至关重要。然而，经典的 Lighthill–Whitham–Richards (LWR) 模型仅提供稳态条件下的均衡值，无法捕获常见的随机变异性，而这些随机变异性是实时交通管理和控制的精确建模的必要组成部分。在本文中，开发了一种随机化自由流速度的随机 LWR (SLWR) 模型，以解释驾驶员异质性引起的随机性，同时保持单个驾驶员的行为恒定。SLWR 模型遵循随机交通密度和流量的守恒定律，并被表述为与时间相关的随机偏微分方程。该模型使用基于空间基础和随机基础的动态双正交（DyBO）方法进行求解。对各种场景进行了模拟并与蒙特卡罗（MC）方法进行了比较，结果表明SLWR模型可以有效地描述动态交通演化并重现一些常见的交通现象。此外，DyBO 方法比 MC 方法显示出显着的计算优势。