Abstract

Vehicular traffic models as complex dynamical systems have been widely studied, yet challenges in obtaining reliable forecasts persist, due to the inherent uncertainty in real-world traffic caused by noises in the measurements, fluctuating demand, unforeseen incidents, and varied driver behaviors. This uncertainty significantly impacts the accuracy and reliability of traffic flow models, making it essential to integrate uncertainty into these models for more realistic solutions.

In this talk, we will focus on investigating the propagation of uncertainties in traffic flow models. Two main approaches to quantify uncertainty will be discussed: non-intrusive methods, such as Monte Carlo techniques, which solve the model for a fixed number of samples using deterministic algorithms, and intrusive methods, like the stochastic Galerkin method, which modify the governing equations to incorporate probabilistic elements. Both methodologies will be presented, highlighting their advantages and limitations, to provide a comprehensive analysis of how they contribute to more accurate and reliable traffic flow predictions.