Unraveling stochastic fundamental diagrams considering empirical knowledge: modeling, limitation and further discussion

Traffic flow modeling relies heavily on fundamental diagrams. However, deterministic fundamental diagrams, such as single or multi-regime models, cannot capture the uncertainty pattern that underlies traffic flow. To address this limitation, a sparse non-parametric regression model is proposed in this paper to formulate the stochastic fundamental diagram. Unlike parametric stochastic fundamental diagram models, a non-parametric model is insensitive to parameters, flexible, and applicable. The computation complexity and the huge memory required for training in the Gaussian process regression have been reduced by introducing the sparse Gaussian process regression. The paper also discusses how empirical knowledge influences the modeling process. The paper analyzes the influence of modeling empirical knowledge in the prior of the stochastic fundamental diagram model and whether empirical knowledge can improve the robustness and accuracy of the proposed model. By introducing several well-known single-regime fundamental diagram models as the prior and testing the model's robustness and accuracy with different sampling methods given real-world data, the authors find that empirical knowledge can only benefit the model under small inducing samples given a relatively clean and large dataset. A pure data-driven approach is sufficient to estimate and describe the pattern of the density-speed relationship.