Influence of Reaction Times and Anticipation on Stability of Vehicular Traffic Flow

Two causes for the instability of traffic flow are investigated: the time lag caused by finite accelerations of vehicles and the delay caused by finite reaction times of drivers. Furthermore, the degree to which drivers may compensate for these delays is simulated by looking several vehicles ahead and anticipating future traffic situations. Since vehicular traffic flow is an extended multiparticle system with many degrees of freedom, two concepts of linear stability have to be considered: (a) local stability of a car following a leader that drives at constant velocity and (b) string (chain) stability of a platoon of several vehicles following each other. Typically, string stability is a much more restrictive criterion than local stability. Both types of stability are simulated with the human driver model of M. Treiber et al. [Physica A, Vol. 360, No. 1, 2006, pp. 71-88], which includes all the foregoing features. Several interesting results were found: (a) with a suitable anticipation, string stability for reaction times exceeding the safety time gap was obtained (to the authors' knowledge, this result had not yet been achieved for any other car-following model); (b) parameter changes that destabilize the model variant with zero reaction time may stabilize the model with finite reaction times, and vice versa; and (c) distributed reaction times (every driver has a different reaction time) can stabilize the system compared with the case of drivers with identical reaction times that are equal to the mean.