Three new models for the flow–density relationship: derivation and testing for freeway and urban data

Three new models for the flow–density relationship are proposed in this work. The resulting flow–density curves are concave in the whole range of feasible values for the parameters. These models have four parameters, three of them being the jam density, the free-flow speed and the kinematic wave speed. The fourth parameter is a shape parameter. The models allow for a great flexibility for fitting of real traffic flow and density data. A remarkable property of these models is the fact that they yield a bilinear fundamental diagram when the shape parameter tends to infinity. The models have been tested with freeway data and urban data. The results demonstrate that the models achieve an excellent goodness of fit and yield realistic estimates of the parameters. The models proposed in this work are a valuable tool not only for fitting flow–density data but also for its use in traffic flow dynamic models.