In this work, a family of finite volume discretization schemes for LWR-type first order traffic flow models (with possible on- and off-ramps) is proposed: the Traffic Reaction Model (TRM). These schemes yield systems of ODEs that are formally equivalent to the kinetic systems used to model chemical reaction networks. An in-depth numerical analysis of the TRM is performed. On the one hand, the analytical properties of the scheme (nonnegative, conservative, capacity-preserving, monotone) and its relation to more traditional schemes for traffic flow models (Godunov, CTM) are presented. Finally, the link between the TRM and kinetic systems is exploited to offer a novel compartmental interpretation of traffic models. In particular, kinetic theory is used to derive dynamical properties (namely persistence and Lyapunov stability) of the TRM for a specific road configuration. Two extensions of the proposed model, to networks and changing driving conditions, are also described.

翻译：本文提出了一类针对LWR型一阶交通流模型（可含入口匝道和出口匝道）的有限体积离散格式家族：交通反应模型（TRM）。这些格式生成的常微分方程组在形式上等价于用于描述化学反应网络的动力学系统。我们对TRM进行了深入的数值分析：一方面，阐述了该格式的解析性质（非负性、守恒性、容量保持性、单调性）及其与传统交通流模型格式（Godunov格式、CTM模型）的关系；另一方面，利用TRM与动力学系统之间的关联，提出了交通模型的创新性舱室化解释。具体而言，运用动力学理论推导了特定道路配置下TRM的动力学性质（包括持久性和李雅普诺夫稳定性）。此外，还描述了该模型在网络化场景和驾驶条件变化场景下的两种扩展形式。