We consider a macroscopic two-phase transition model for vehicular traffic flow subject to a point constraint on the density flux. The two phases correspond to light and heavy traffic and their dynamics are described respectively by the Lighthill–Whitham–Richards model and the Aw–Rascle–Zhang model. Their intersection, the so-called metastable phase, is assumed to be non empty. The discrete in time point constraint mechanism, inducing flux limitation at bottlenecks, is explored within this two-phase model. We introduce a new definition of admissible solutions for the Cauchy problem, for which we prove existence and we provide a characterization. In particular, these admissible solutions attain the maximal flux allowed by the constraint whenever it is enforced, which guarantees compatibility of the constructed solutions with the modeling assumption imposed at the level of the Riemann solver. These results rely on the wave-front tracking method and on adaptation of the specific entropies and renormalization properties introduced in Andreainov, Donadello, Rosini, M3AS (2016) while dealing with the Aw–Rascle–Zhang model with point constraint.

我们考虑了一个针对交通流量的宏观两阶段过渡模型，该模型受密度通量的点约束。这两个阶段分别对应于轻便和繁忙交通，其动力学分别由Lighthill-Whitham-Richards模型和Aw-Rascle-Zhang模型描述。它们的交点，即所谓的亚稳相，被假定为非空的。在此两阶段模型中，探索了离散的时间点约束机制，该机制会导致瓶颈处的磁通量限制。我们引入了柯西问题的可容许解的新定义，为此我们证明了存在并提供了一个特征。尤其是，这些强制解决方案无论何时强制执行都会达到约束所允许的最大通量，这样可以保证构造的解决方案与在黎曼求解器级别施加的建模假设兼容。这些结果依赖于波前跟踪方法以及特定熵的适应性和引入到的重归一化特性。Andreainov，Donadello，Rosini，M3AS（2016年），同时处理具有点约束的Aw-Rascle-Zhang模型。