Two 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 third parameter is a shape parameter. The models allow for enough 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 havebeen tested with freeway data and urban data. The urban flow-density model fits data collected on an urban zone. This model lies on the assumption of the existence of a macroscopic or urban fundamental diagram, which has been recently shown by several authors. 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 notonly for fitting flow-density data but also for its use in traffic flow dynamic models.
Abstract