We consider hyperbolic partial differential equations (PDEs) for a dynamic description of the traffic behavior in road networks. These equations are coupled to a Hawkes process that models traffic accidents taking into account their self-excitation property which means that accidents are more likely in areas in which another accident just occurred. We discuss how both model components interact and influence each other. A data analysis reveals the self-excitation property of accidents and determines further parameters. Numerical simulations using risk measures underline and conclude the discussion of traffic accident effects in our model.

翻译：我们考虑采用双曲型偏微分方程（PDE）对道路网络中的交通行为进行动态描述。这些方程与一个霍克斯过程相耦合，该过程用于对交通事故进行建模，并考虑了事故的自激励特性，即事故在刚发生过另一事故的区域更可能发生。我们讨论了这两个模型组件如何相互作用与影响。数据分析揭示了事故的自激励特性并确定了其他参数。利用风险度量的数值模拟进一步证实并总结了模型中交通事故影响的讨论。