Based on the BLN boundary conditions, the paper proves that local traffic supply and demand define the boundary conditions for the LWR model. A rigorous methodology for intersection modeling within the LWR framework is proposed, based on the supply/demand concept and the Riemann problem for nodes. The invariance principle is shown to be necessary for intersection models to be consistent. Two models, the equilibrium and the optimization model, are introduced which satisfy the invariance principle. Analytical solutions are given for the merge and diverge models, and in these special cases optimization and equilibrium model are shown to be equivalent and analytically tractable. The merge model is shown to be compatible with experimental data, and to predict wide scatter of flow plots. Finally, the analysis of the Riemann problem for the multicommodity FIFO LWR model makes it possible to specify composition dynamics and boundary data. Thus the intersection models, the boundary data and the flow models can be combined into a single network traffic flow model. Future research should include modeling of heterogeneous traffic for non FIFO intersection modeling, as well as carrying out experimental tests for intersection models.
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