In this paper a novel non-negative finite volume discretization scheme is proposed for certain first order nonlinear partial differential equations describing conservation laws arising in traffic flow modelling. The spatially discretized model is shown to preserve several fundamentally important analytical properties of the conservation law (e.g., conservativeness, capacity) giving rise to a set of (second order) polynomial ODEs. Furthermore, it is shown that the discretized traffic flow model is formally kinetic and that it can be interpreted in a compartmental context. As a consequence, traffic networks can be represented as reaction graphs. It is shown that the model can be equipped with on- and off- ramps in a physically meaningful way, still preserving the advantageous properties of the discretization. Numerical case studies include empirical convergence tests, and the stability analysis presented in the paper paves the way to scalable observer and controller design.

翻译：在本文中,为描述交通流量建模产生的养护法的一阶非线性部分偏差方程式提出了一个新的非负性有限量分解办法,空间分解模型显示,该模型保留了养护法的若干具有根本重要性的分析特性(例如,保守性、能力),产生了一套(第二顺序)多式ODE;此外,还表明,离散交通流量模型形式上是动能的,可以在一个区间背景下加以解释;因此,交通网络可以作为反应图来代表;该模型可以具有实际意义的方式装设起起起起落坡道和起落坡道,仍然保留离散法的有利特性;数量案例研究包括实证的趋同试验,以及文件中的稳定性分析为可缩缩放的观察员和控制器设计铺平了道路。