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

Simone Göttlich, Thomas Schillinger

TL;DR

Hyperbolic partial differential 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.

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.

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

TL;DR

Hyperbolic partial differential 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.

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.
Paper Structure (20 sections, 2 theorems, 49 equations, 14 figures, 3 tables, 1 algorithm)

This paper contains 20 sections, 2 theorems, 49 equations, 14 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Traffic accident model on a single road
  3. Influence of accidents on traffic flow dynamics
  4. Influence of traffic on accidents
  5. Traffic accident network model
  6. 1-2 junction
  7. 2-1 junction
  8. Influence of accidents on traffic flow on networks
  9. Influence of traffic on accidents on networks
  10. Accidents at the junction
  11. Numerical experiments
  12. Accident analysis
  13. Risk Measures
  14. Total travel time
  15. Number of accidents
  16. ...and 5 more sections

Key Result

Lemma 2.2

Let $f$ be a LWR-flux, i.e. $f(0)=f(1) = 0$, being strictly concave and assume that there exists a unique $\rho^* \in (0,1)$ such that $f'(\rho^*)=0$. Assume that $c_\text{a}(\cdot,t)c_{\text{road}}(\cdot) \in C^2({[a,b]})\cap TV({[a,b]})$. Furthermore, we assume that $c_\text{a}(\cdot)c_{\text{road

Figures (14)

  • Figure 1: Comparison of intermediate accident times with different shares of self-excitation accidents.
  • Figure 2: Intermediate accident times for accidents in southern Great Britain in 2018.
  • Figure 3: The Hawkes processes $N(t)$ to the left and the corresponding conditional intensity functions $\lambda^*$ to the right, with $\mu_1$, $\lambda_1$ in the first row and $\mu_2$ and $\lambda_2$ in the second row.
  • Figure 4: Data comparison of the three parameters compared to an optimal fit for exponential distributions (distance and duration) and Beta distribution (accident severity). Left the accident size, in the middle the accident duration and to the right the accident severity.
  • Figure 5: The diamond traffic model.
  • ...and 9 more figures

Theorems & Definitions (5)

  • Definition 2.1
  • Lemma 2.2
  • Definition 2.3
  • Lemma 2.4
  • Remark 3.1