Criteria for convective versus absolute string instability in car-following models

The linear stability properties of car-following models of highway traffic are analysed. A general family of models is introduced and the subsequent analysis developed in terms of its partial derivatives. Two measures of wave propagation, namely (i) the group velocity and (ii) the signal velocity, are introduced and computed. These measures are used to classify how instability propagates disturbances, measured relative to the frame of the road along which the vehicles drive. Detector data suggest that disturbances should propagate only in an upstream direction (convective upstream instability), and it is shown how to parametrize models to agree with data and avoid unrealistic downstream propagation (absolute and convective downstream instability).