Analytical formulation for explaining the variations in traffic states: A fundamental diagram modeling perspective with stochastic parameters

Qixiu Cheng, Yuqian Lin, Xuesong Simon Zhou, Zhiyuan Liu

Abstract: Highlights•An analytical and quantitative method to analyze traffic state variations.•Two stochastic fundamental diagrams with lognormal and skew-normal distributions.•Reproduce scatters in the traffic flow fundamental diagrams.•Stochastic freeway capacity analysis with closed forms.•Tracing the sources of stochasticity in freeway capacity with stochastic fundamental diagram.