A macro traffic flow model accounting for real-time traffic state

•A traffic flow model with real-time traffic state is proposed.•The effects of real-time traffic state on uniform flow are explored.•The effects of real-time traffic state on small perturbation are studied.

In this paper, we propose a traffic flow model to study the effects of the real-time traffic state on traffic flow. The numerical results show that the proposed model can describe oscillation in traffic and stop-and-go traffic, where the speed–density relationship is qualitatively accordant with the empirical data of the Weizikeng segment of the Badaling freeway in Beijing, which means that the proposed model can qualitatively reproduce some complex traffic phenomena associated with real-time traffic state.