Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms. The hyperbolic main part of these models turns out to have several favourable features. In particular, we determine Riemann invariants and prove richness and total linear degeneracy of the hyperbolic systems. Moreover, a physically reasonable invariant domain is obtained for all equations of the hierarchy. Additionally, we investigate the full relaxation system with respect to stability and persistence of periodic (stop and go type) solutions and derive a condition for the appearance of such solutions. Finally, numerical results for various situations are presented, illustrating the analytical findings.

翻译：从非局部版本的Prigogine-Herman交通模型出发，我们推导出一个由带松弛项的拟线性双曲型方程组构成的动力学离散速度交通流模型的自然层次结构。这些模型的双曲主体部分展现出若干有利特征。特别地，我们确定了黎曼不变量，并证明了双曲系统的丰富性与完全线性退化性质。此外，对于该层次结构中的所有方程，均获得了物理合理的不变域。同时，我们针对周期型（走走停停型）解的稳定性和持续性研究了完整松弛系统，并推导出此类解出现的条件。最后，通过多种情形下的数值结果验证了理论分析结论。