Uncertainty quantification in a macroscopic traffic flow model calibrated on GPS data.

Area of Science:

• Traffic Flow Dynamics
• Mathematical Modeling
• Uncertainty Quantification

Background:

• The Lighthill-Whitham-Richards model is a cornerstone of traffic flow theory.
• Deterministic models often fail to capture real-world traffic variability.
• Understanding uncertainty is crucial for robust traffic management.

Purpose of the Study:

• To integrate random parameters into the Lighthill-Whitham-Richards traffic flow model.
• To develop and apply a semi-intrusive method for uncertainty propagation analysis.
• To validate the proposed approach using empirical traffic data.

Main Methods:

• Incorporation of stochastic elements into the deterministic Lighthill-Whitham-Richards equations.
• Implementation of a semi-intrusive uncertainty quantification technique.
• Validation against real-world traffic data from vehicle GPS systems (Autoroutes Trafic).

Main Results:

• Successfully integrated random parameters into the traffic flow model.
• Quantified uncertainty propagation using the semi-intrusive approach.
• Demonstrated the method's validity through comparison with empirical GPS data.

Conclusions:

• The enhanced Lighthill-Whitham-Richards model with random parameters effectively captures traffic variability.
• Semi-intrusive methods provide a viable approach for uncertainty quantification in traffic models.
• Validation with real-world data confirms the practical applicability of the developed technique.