Empirical basis for car-following theory development

By analyzing data from a car-following experiment, it is shown that drivers control their car by a simple scheme. The acceleration $a(t)$ is held approximately constant for a certain time interval, followed by a jump to a new acceleration. These jumps seem to include a deterministic and a random component; the time $T$ between subsequent jumps is random, too. This leads to a dynamic, that never reaches a fixed-point ($a(t) \to 0$ and velocity difference to the car in front $\Delta v \to 0$) of the car-following dynamics. The existence of such a fixed-point is predicted by most of the existing car-following theories. Nevertheless, the phase-space distribution is clustered strongly at $\Delta v=0$. Here, the probability distribution in $\Delta v$ is (for small and medium distances $\Delta x$ between the cars) described by $p(\Delta v) \propto \exp(-|\Delta v|/\Delta v_0)$ indicating a dynamic that attracts cars to the region with small speed differences. The corresponding distances $\Delta x$ between the cars vary strongly. This variation might be a possible reason for the much-discussed widely scattered states found in highway traffic.