Transportation Link Risk Analysis Through Stochastic Link Fundamental Flow Diagram

This paper proposes a method for assessing societal risk along a traffic link by integrating a stochastic formulation of the fundamental diagram. The approach accounts for uncertainty in vehicle speed due to user heterogeneity, vehicle characteristics, and environmental conditions. The risk index is decomposed into occurrence, vulnerability, and exposure components, with the occurrence probability modeled as a function of stochastic speed. The inverse gamma distribution is adopted to represent speed variability, enabling analytical tractability and control over dispersion. Numerical results show that urban and suburban environments exhibit distinct sensitivity to model parameters, particularly the gamma shape parameter η and the composite parameter c = β · v0 obtained by the product of the occurrence parameter β and the free speed flow v0. Graphical representations illustrate the impact of uncertainty on risk estimation. The proposed framework enhances existing deterministic methods by incorporating probabilistic elements, offering a foundation for future applications in traffic safety management and infrastructure design.