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 occured. 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.

In this article, we consider transport networks with uncertain demands. Network dynamics are given by linear hyperbolic partial differential equations and suitable coupling conditions, while demands are incorporated as solutions to stochastic differential equations. For the demand satisfaction, we solve a constrained optimal control problem. Controls in terms of network inputs are then calculated explicitly for different assumptions. Numerical simulations are performed to underline the theoretical results.