Memory effects in microscopic traffic models and wide scattering in flow-density data

By means of microscopic simulations we show that noninstantaneous adaptation of the driving behavior to the traffic situation together with the conventional method to measure flow-density data provides a possible explanation for the observed inverse-lambda shape and the wide scattering of flow-density data in "synchronized" congested traffic. We model a memory effect in the response of drivers to the traffic situation for a wide class of car-following models by introducing an additional dynamical variable (the "subjective level of service") describing the adaptation of drivers to the surrounding traffic situation during the past few minutes and couple this internal state to parameters of the underlying model that are related to the driving style. For illustration, we use the intelligent-driver model (IDM) as the underlying model, characterize the level of service solely by the velocity, and couple the internal variable to the IDM parameter "time gap" to model an increase of the time gap in congested traffic ("frustration effect"), which is supported by single-vehicle data. We simulate open systems with a bottleneck and obtain flow-density data by implementing "virtual detectors." The shape, relative size, and apparent "stochasticity" of the region of the scattered data points agree nearly quantitatively with empirical data. Wide scattering is even observed for identical vehicles, although the proposed model is a time-continuous, deterministic, single-lane car-following model with a unique fundamental diagram.