The fundamental diagram, which is the graphical representation of the relationships among traffic flow, speed, and density, has been the foundationof traffic flow theory and transportation engineering. After 75 years since the seminal Greenshields model, a variety of models have been proposed to mathematically represent the speed-density relationship which underliesthe fundamental diagram. Observed in these models was a clear path towardtwo competing goals: mathematical elegance and empirical accuracy. As thelatest development of such a pursuit, this paper presents a family of speed-density models with varying number of parameters. All of these models perform satisfactorily with physically meaningful parameters. In addition, speed variation is accounted for as traffic density varies and 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.
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