Logistic modeling of the equilibrium speed–density relationship

The fundamental diagram, as the graphical representation of the relationships among traffic flow, speed, and density, has been the foundation of traffic flow theory and transportation engineering. Seventy-five years after the seminal Greenshields model, a variety of models have been proposed to mathematically represent the speed–density relationship which underlies the fundamental diagram. Observed in these models was a clear path toward two competing goals: mathematical elegance and empirical accuracy. As the latest development of such a pursuit, this paper presents a family of speed–density models with varying numbers of parameters. All of these models perform satisfactorily and have physically meaningful parameters. In addition, speed variation with traffic density is accounted for; this enables statistical approaches to traffic flow analysis. The results of this paper not only improve our understanding of traffic flow but also provide a sound basis for transportation engineering studies.

► We used a generalized logistic growth curve to model the equilibrium speed-density relationship which is the key to the fundamental diagram of traffic flow.
► The proposed five-parameter logistic speed-density model achieves both mathematical elegance and empirical accuracy which is deemed to be hard to achieve simultaneously.
► The numerical relative error showed that the proposed model yields the smallest error among the models compared.
► The validation results using empirical data from a different site revealed the transferability of the proposed model.