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The wide scattering nature of the fundamental diagram (FD) with observed flow-density data may be associated with the dynamical traffic flow process, especially on signalized intersection. To describe the uncertainty of FD, in this work we established stochastic fundamental diagram (SFD) which is defined by the distributions of shockwave speed. Our approach is based on a two-level stochastic process of the traffic flow system in terms of the dynamics of traffic density and state mode associated with signal phases which is named switching linear dynamical systems (SLDS). Then, variational Bayesian learning method is adopted to compute the distributions of SFD parameter to approximate the experimental distributions of shockwave calculated by the observed flow-density data. Given traffic flow data from the NGSIM program, the verification result demonstrated that the SFD can be more helpful to capture the main features of the observed widely scattering of the flow-density data compared with FD. With the shockwave speed sampled from the SFD, the SLDS could describe the dynamic characteristics of traffic flow and be applied to the maximum likelihood estimation of traffic density or flow rate. Because it is simple and automatically calculated, the SFD provides an alternative description for fundamental diagram and its uncertainty in the traffic flow.

Empirical Approximation for the Stochastic Fundamental Diagram of Traffic Flow on Signalized Intersection