First-Order Macroscopic Traffic Flow Models: Intersection Modeling, Network Modeling

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A Hamilton-Jacobi approach to junction problems and application to traffic flows (2011, unknown): “For η = ( η 1 , ..., η N ) ∈ ( R + ) N , we set Because u is continuous at ( t 0 , 0), we get for η ∈ ( R + ∗ ) N that M η → M 0 = 0 ( t η , x η ) → ( t 0 , 0) as soon as one of the component η i 0 → 0.”
A kinematic wave theory of multi-commodity network traffic flow (2012, background): “Such diverging and merging rules have been verified by observations at the aggregate level (Muñoz and Daganzo, 2002; Lebacque, 2005; Ni and Leonard, 2005; Cassidy and Ahn, 2005; Bar-Gera and Ahn, 2010).”
Continuous formulations and analytical properties of the link transmission model (2014, methodology): “In addition, LTM was also shown to yield much more accurate solutions than CTM with the same time-step size.”