Empirical basis for car-following theory development

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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) → 0 and velocity difference to the car in front Δv → 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 Δv=0. Here, the probability distribution in Δv is (for small and medium distances Δx between the cars) described by p(Δv) ∝ (-|Δv|/Δv₀) indicating a dynamic that attracts cars to the region with small speed differences. The corresponding distances Δx between the cars vary strongly. This variation might be a possible reason for the much-discussed widely scattered states found in highway traffic.