Traffic is loopy- Insights and findings about traffic state hysteresis

Traffic state hysteresis has confounded traffic flow theory for decades. While the literature typically assumes there is a single hysteresis mechanism, we show there are four distinctly different hysteresis mechanisms that have been conflated with each other in the literature and demonstrate another hysteresis mechanism that has not been actively discussed. This paper shows the acceleration hysteresis: (1) should be expected whenever a driver responds with a delay to their leader, (2) should continually perturb the measured traffic state away from the equilibrium fundamental diagram, FD, and (3) is implicit in many traffic flow models. When the state is perturbed, the models continue to employ an unseen equilibrium FD, but because equilibrium states are rarely seen in traffic measurements it should be challenging to establish the equilibrium FD, e.g., potentially having to impute the FD. These findings also suggest a new perspective for higher order models: in addition to capturing driver behavior they could control for how acceleration distorts traffic measurements. After discussing the hysteresis mechanisms, this paper uses naturalistic driving data to explore the two mechanisms that can distort the measured FD: acceleration hysteresis and grade hysteresis. The results suggest that acceleration modulates jam spacing while grade modulates driver response time and the impacts of acceleration. Furthermore, when vehicles come to a stop, the stopped spacing retains the preceding deceleration conditions, resulting in a non-equilibrium state. Thus, one should not use the stopped spacing to calibrate car following models unless they are designed to account for the acceleration hysteresis.