A new approach for modeling of fundamental diagrams

According to the intra-vehicle interaction, a traffic flow can generally be divided into three homogeneous states (1) that of free driving, (2) that of bunched driving, and (3) that of standing. The parameter describing the state of free driving is the desired speed, for the estate of bunching it is the intra-vehicle gaps (time headway) within the convoy and the mean speed of the convoy, and for the state of standing it is the maximum jam density. These are the most essential parameters which do not depend on the actual traffic situation. This paper introduces a new model which considers the Fundamental Diagram (equilibrium speed–flow–density relationship) as a function of the homogeneous states. All traffic situations in reality can be considered as combinations of the homogeneous states and therefore can be described by the essential parameters mentioned above. The non-congested (fluid) traffic is a combination (superposition) of the states of free driving and bunched driving, the congested (jam, stop, and go) traffic is a combination of the states of bunched driving (go) and standing (stop). The contribution of the traffic states within the differently congested traffic situations can then be easily obtained from the queueing and probability theory. As a result, Fundamental Diagram in all equilibrium traffic situations is derived as simple functions of the essential parameters. According to the new model the capacity of freeways and rural highways can be determined by measuring the essential parameters. This is much easier than measuring the capacity directly. Furthermore, the probabilities of the various traffic states can be obtained from the new model. This leads to new possibilities in real-time controlling and telematics. The new model is verified by comprehensive measurements carried out on freeways and rural highways in Germany.