Understanding widely scattered traffic flows, the capacity drop, platoons, and times-to-collision as effects of variance-driven time gaps

We investigate the adaptation of the time headways in car-following models as a function of the local velocity variance, which is a measure of the inhomogeneity of traffic flow. We apply this mechanism to several car-following models and simulate traffic breakdowns in open systems with an on-ramp as bottleneck. Single-vehicle data generated by several 'virtual detectors' show a semi-quantitative agreement with microscopic data from the Dutch freeway A9. This includes the observed distributions of the net time headways and times-to-collision for free and congested traffic. While the times-to-collision show a nearly universal distribution in free and congested traffic, the modal value of the time headway distribution is shifted by a factor of about two in congested conditions. Macroscopically, this corresponds to the 'capacity drop' at the transition from free to congested traffic. Finally, we explain the wide scattering of one-minute flow-density data by a self-organized variance-driven process that leads to the spontaneous formation and decay of long-lived platoons even for deterministic dynamics on a single lane.