Spacing-speed dependency on relative speeds to the adjacent lanes: a statistical test

The spacing of a vehicle is the spatial separation between this vehicle and the vehicle ahead. It forms the basis of the fundamental diagram of traffic flow. Traditional car-following models assume that the spacing of a following vehicle is strictly a function of the speed of the lead vehicle in the same lane. The recent literature, however, reports a phenomenon of spacing-speed dependency on the relative speeds to the adjacent lanes, termed speed differential effect. The aim of this paper is to statistically test the speed differential effect. To quantitatively measure the speed differential effect, we develop a mixture spacing-speed model to capture the probabilistic nature of the spacing and speed relationship, and then relate this spacing-speed relation to the relative speeds to the adjacent lanes. We apply the developed model to test the speed differential effect. Our empirical analysis provides strong statistical evidence to support the speed differential effect.