INFLUENCE OF REACTION TIMES AND ANTICIPATION ON THE STABILITY OF VEHICULAR TRAFFIC FLOW

Abstract

We investigate two causes for the instability of traffic flow: The time lag caused by finite accelerations of the vehicles, and the delay caused by the finite reaction times of the drivers. Furthermore, we simulate to which degree drivers may compensate for these delays by looking several vehicles ahead and anticipate future traffic situations. Since vehicular traffic flow is a multi-particle system with many degrees of freedom, two concepts of linear stability have to be considered: Local stability of a car following a leader that drives at constant velocity, and string (chain) stability of a “platoon” of several vehicles following each other. Typically, string stability is a much more restrictive criterion than local stability. We simulate both types of stability with the human driver model (HDM)[M. Treiber et al., Physica A, Vol. 360 (1), 71–88 (2006)], which includes all the features above. We found several remarkable results: (i) with a suitable anticipation, we obtained string stability for reaction times exceeding the “safe time headway”, which, to date, has not yet been obtained for any other car-following model; (ii) parameter changes that destabilize the model variant with zero reaction time may stabilize the model with finite reaction times and vice versa, (iii) distributed reaction times (every driver has a different reaction time) can stabilize the system compared to drivers with identical reaction times that are equal to the mean.