Influence of reaction times and anticipation on the stability of vehicular traffic flow
Time Delay Systems, Volume # 6 | Part# 1
Arne Kesting; Martin Treiber
Digital Object Identifier (DOI)
car-following model,microscopic traffic simulation,human reaction time,time-delayed system,local and string stability
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.
 Bando, M., K. Hasebe, K. Nakanishi and A. Nakayama (1998). Analysis of optimal velocity model with explicit delay. Phys. Rev. E 58, 5429.  Brackstone, M. and M. McDonald (1999). Car-following: a historical review. Transportation Research F 2, 181-196.  Brogan, William L. (1991). Modern control theory. Prentice-Hall. Upper Saddle River, USA.  Davis, L. C. (2002). Modifications of the optimal velocity traffic model to include delay due to driver reaction time. Physica A 319, 557.  Green, Marc (2000). 'How long does it take to stop?' methodological analysis of driver perception-brake times. Transportation Human Factors 2, 195-216.  Helbing, D. (2001). Traffic and related self-driven many-particle systems. Reviews of Modern Physics 73, 1067-1141.  Holland, E. N. (1998). A generalised stability criterion for motorway traffic. Transportation Research B 32, 141-154.  Isidori, Alberto (1995). Nonlinear Control Systems. Springer. New York.  Kesting, A., M. Treiber, M. Schönhof, F. Kranke and D. Helbing (2006). Jam-avoiding adaptive cruise control (ACC) and its impact on traffic dynamics. In: Traffic and Granular Flow'05. Springer. Berlin. preprint physics/0601096.  Knospe, W., L. Santen, A. Schadschneider and M. Schreckenberg (2002). Single-vehicle data of highway traffic: Microscopic description of traffic phases. Phys. Rev. E 65, 056133.  Newell, G. F. (1961). Nonlinear effects in the dynamics of car following. Operations Research 9, 209.  Shiffrin, R. and W. S. Schneider (1977). Controlled and automatic human information processing ii: Perceptual learning, automatic attending, and a general theory. Psychological Review 84, 127- 190.  Tilch, B. and D. Helbing (2000). Evaluation of single vehicle data in dependence of the vehicle-type, lane, and site. In: Traffic and Granular Flow'99 (D. Helbing, H. J. Herrmann, M. Schreckenberg and D. E. Wolf, Eds.). pp. 333-338. Springer. Berlin.  Treiber, M., A. Hennecke and D. Helbing (1999). Derivation, properties, and simulation of a gas-kinetic-based, non-local traffic model. Phys. Rev. E 59, 239-253.  Treiber, M., A. Hennecke and D. Helbing (2000). Congested traffic states in empirical observations and microscopic simulations. Phys. Rev. E 62, 1805-1824.  Treiber, M., A. Kesting and D. Helbing (2006). Delays, inaccuracies and anticipation in microscopic traffic models. Physica A 360, 71-88.