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We propose a framework for constructing microscopic traffic models frommicroscopic acceleration patterns that can in principle be experimentalmeasured and proper averaged. The exact model thus obtained can be used tojustify the consistency of various popular models in the literature. Assuminganalyticity of the exact model, we suggest that a controlled expansion aroundthe constant velocity, uniform headway "ground state" is the proper way ofconstructing various different effective models. Assuming a unique ground statefor any fixed average density, we discuss the universal properties of theresulting effective model, focusing on the emergent quantities of the couplednon-linear ODEs. These include the maximum and minimum headway that give thecoexistence curve in the phase diagram, as well as an emergent intrinsic scalethat characterizes the strength of interaction between clusters, leading tonon-trivial cluster statistics when the unstable ground state is randomlyperturbed. Utilizing the universal properties of the emergent quantities, asimple algorithm for constructing an effective traffic model is also presented.The algorithm tunes the model with statistically well-defined quantitiesextracted from the flow-density plot, and the resulting effective modelnaturally captures and predicts many quantitative and qualitative empiricalfeatures of the highway traffic, especially in the presence of an on-rampbottleneck. The simplicity of the effective model provides strong evidence thatstochasticity, diversity of vehicle types and modeling of complicatedindividual driving behaviors are \emph{not} fundamental to many observations ofthe complex spatiotemporal patterns in the real traffic dynamics. We alsopropose the nature of the congested phase can be well characterized by the longlasting transient states of the effective model, from which the wide movingjams evolve.

Non-linear Dynamics, Emergent Behaviors and Controlled Expansions: Towards Effective Modeling of the Congested Traffic