This paper investigates advanced continuum models for describing traffic dynamics at congested flows. First, the existing high-order models are reviwed and discussed, and a new formulation is proposed which does not require the use of an equilibrium speed-density relationship. (A model is of high-order when it includes both mass and momentum conservation.) Traffic friction at interrupted flows and changing geometries is also addressed through the use of a viscosity term. The model is then discretized through two alternative numerical schemes to examine the effectiveness of the implementation. Stability analysis is performed to set up numerical limits of the model parameters. Finally, in two test cases with congested and uncongested field data, the new model is compared with the existing models; this comparison suggests that the proposed mode is more accurate and computationally more efficient.
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Acknowledgements-Thaeu thors would like to thank A. Chronopoulos from the University of Minnesota and R. Plum from Minneapolis Traffic Engineering for their valuable input in conducting the research. Financial support for this research was provided by Minnesota Department of Transportation.