@article{ref1,
title="Logistic modeling of the equilibrium speed-density relationship",
journal="Transportation research part A: policy and practice",
year="2011",
author="Wang, Haizhong and Li, Jia and Chen, Qian-Yong and Ni, Daiheng",
volume="45",
number="6",
pages="554-566",
abstract="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.<p />",
language="en",
issn="0965-8564",
doi="10.1016/j.tra.2011.03.010",
url="http://dx.doi.org/10.1016/j.tra.2011.03.010"
}