A stochastic approach to the flow-concentration curve in traffic flow theory

An alternative stochastic model for the fundamental diagram of traffic flow with minimal number of parameters is proposed. The key features of the model lie in its “catastrophic” potential function as well as the stochastic nature, which makes it possible to describe the main features of the flow-concentration relation. In particular, the inverse-λ shape as well as the wide scattering of congested traffic data are both reproduced. In our model, the inverse-λ shape and the associated sudden jump of physical quantities arise due to the existence of two simultaneous stable traffic flow states and the scattering of the data, on the other hand, is attributed to the noise terms introduced in the stochastic differential equations. The model parameters are then calibrated and compared qualitatively with the data. It is shown that both the fundamental diagram and its variance are reasonably reproduced.