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

By means of microscopic simulations we show that non-instantaneous adaptation of the driving behaviour to the traffic situation together with the conventional measurement method of flow-density data can explain 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 a new dynamical variable describing the adaptation of drivers to the surrounding traffic situation during the past few minutes (``subjective level of service'') 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 underlying model, characterize the level of service solely by the velocity and couple the internal variable to the IDM parameter ``netto time gap'', modelling an increase of the time gap in congested traffic (``frustration effect''), that is supported by single-vehicle data. % We simulate open systems with a bottleneck and obtain flow-density data by implementing ``virtual detectors''. Both 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.