Data-inspired modeling of accidents in traffic flow networks using the Hawkes process

TL;DR

This paper introduces a novel traffic flow model combining hyperbolic PDEs with a Hawkes process to capture the self-excitation nature of traffic accidents, supported by data analysis and numerical simulations.

Contribution

It presents a new integrated modeling framework that couples PDE-based traffic flow with a Hawkes process for accident dynamics, highlighting their interaction and impact.

Findings

Accidents exhibit self-excitation behavior in traffic networks.

Data analysis quantifies parameters for the Hawkes process.

Simulations demonstrate the influence of accidents on traffic flow risk.

Abstract

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.