Unraveling stochastic fundamental diagrams with empirical knowledge: Modeling, limitations, and future directions

Traffic flow modeling relies heavily on fundamental diagrams. However, deterministic fundamental diagrams, such as single or multi-regime models, cannot capture the underlying uncertainty in traffic flow. To address this limitation, this study proposes a non-parametric Gaussian process model to formulate the stochastic fundamental diagram. Unlike parametric models, the non-parametric approach is insensitive to parameters, flexible, and widely applicable. The computational complexity and high memory requirements of Gaussian process regression are also mitigated by introducing sparse Gaussian process regression. This study also examines the impact of incorporating empirical knowledge into the prior of the stochastic fundamental diagram model and assesses whether such knowledge can enhance the model’s robustness and accuracy. By using several well-known single-regime fundamental diagram models as priors and testing the model’s performance with different sampling methods on real-world data, this study finds that empirical knowledge benefits the model only when small inducing samples are used with a relatively clean and large dataset. In other cases, a purely data-driven approach is sufficient to estimate and describe the density–speed relationship pattern.