[Paper Review] Data-Driven Models for Traffic Flow at Junctions

Michaël Herty, Niklas Kolbe|arXiv (Cornell University)|Jan 1, 2022

Traffic Prediction and Management Techniques1 citations

TL;DR

This paper proposes a data-driven machine learning framework that integrates artificial neural networks with parametrized Riemann solvers to derive accurate, consistent coupling conditions for macroscopic traffic flow models at road junctions. By training on real vehicle trajectory data, the model outperforms classical flow-maximization rules in predicting realistic traffic dynamics, including congestion and prioritization effects not captured by traditional models.

ABSTRACT

The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based on real-world car trajectory data we propose a new class of data-driven models with the requirements of being consistent to networked hyperbolic traffic flow models. To this end the new models combine artificial neural networks with a parametrization of the solution space to the half-Riemann problem at the junction. A method for deriving density and flux corresponding to the traffic close to the junction for data-driven models is presented. The models parameter are fitted to obtain suitable boundary conditions for macroscopic first and second-order traffic flow models. The prediction of various models are compared considering also existing coupling rules at the junction. Numerical results imposing the data-fitted coupling models on a traffic network are presented exhibiting accurate predictions of the new models.

Motivation & Objective

• To develop data-consistent coupling conditions for macroscopic traffic flow models on road networks.
• To address the lack of validation of macroscopic models against real-world trajectory data, especially at junctions.
• To improve upon classical coupling rules—based on flow maximization—that fail to capture complex traffic phenomena like ramp prioritization and congestion propagation.
• To provide a unified framework for training machine learning models that are mathematically consistent with hyperbolic conservation laws and networked PDE systems.
• To validate the proposed models using real trajectory data from an on-ramp junction, including long-term simulations and throughput comparisons.

Proposed method

• Uses vehicle trajectory data from a freeway on-ramp to derive macroscopic densities and fluxes via control volume tracking.
• Normalizes data using a time-delay correction based on Kirchhoff’s condition to account for interaction synchronization and diurnal variability.
• Estimates road-specific fundamental diagrams (speed vs. density) from the normalized data.
• Proposes a novel class of machine learning models combining artificial neural networks with a parametrized solution space of the half-Riemann problem at junctions.
• Employs an evolutionary algorithm and stochastic gradient descent to train model parameters, ensuring consistency with macroscopic PDE models.
• Implements finite-volume schemes to simulate network dynamics and compare predictions across models.

Experimental results

Research questions

• RQ1 Can machine learning models trained on real trajectory data produce more accurate and realistic coupling conditions at traffic junctions than classical flow-maximization rules?
• RQ2 How can data-driven models be made mathematically consistent with hyperbolic conservation laws and networked PDE systems?
• RQ3 To what extent can data-driven coupling models predict phenomena such as congestion and ramp prioritization not present in training data?
• RQ4 How does model depth (number of layers) affect the realism and accuracy of traffic flow predictions in network simulations?
• RQ5 Can a unified framework be established that integrates data-fitted fundamental diagrams with data-driven coupling rules in a consistent macroscopic modeling framework?

Key findings

• The data-driven machine learning models achieved a better fit to both training and test data than classical coupling rules, particularly in capturing complex traffic dynamics.
• Single-layer neural network models produced unrealistic results, such as complete junction blockage, highlighting the need for deeper architectures.
• Four-layer neural network models produced boundary flux predictions as accurate as the best classical models in throughput prediction tests.
• In congestion prediction scenarios—where training data was sparse—the data-driven models correctly predicted strong prioritization of on-ramp traffic, unlike classical models which failed to reflect such behavior.
• The proposed framework successfully normalized trajectory data using time-delay adjustments based on Kirchhoff’s condition, improving consistency with macroscopic flow laws.
• The integration of learned coupling conditions with finite-volume schemes produced stable and realistic network-level traffic dynamics, validating the approach for real-world applications.