A variational formulation of kinematic waves: Solution methods

By Carlos F. Daganzo. 2005

193 citations recorded by the source corpus.

Subfields: Building and Construction, Control and Systems Engineering, Transportation

View Paper: https://www.semanticscholar.org/paper/6f06663c94270efabba1add1c492104b1faac72b

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In Building and Construction

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Citations in the corpus

The Hamilton-Jacobi Partial Differential Equation and the Three Representations of Traffic Flow (2013, background): “6d illustrates how the ξ−’s are related under this assumption.258 259 As pointed out in Daganzo (2005a); Leclercq et al. (2007) in the con-260 text of the N- and X-model, bottlenecks (fixed and moving) can be added261 as “shortcuts” to the solution network.”
Traffic state estimation on highway: A comprehensive survey (2017, methodology): “…with triangular FD, known as Newell’s minimization principle and variational theory (VT) within the transportation community (Newell, 1993a,b,c; Daganzo, 2005a,b), a method that can manage internal boundary conditions based on the HL formula (Claudel and Bayen, 2010a,b), and an exact method…”
Lane-changing in traffic streams (2006, methodology): “It was postulated in Michalopoulos et al. (1984) that U‘ was a linear function of the set of k‘ s, but the idea was not applied successfully at the time because effective numerical methods (Daganzo, 1993, 2005b; Lebacque, 1996; Daganzo et al., 1997) had not yet been developed.”
Continuous formulations and analytical properties of the link transmission model (2014, methodology): “In (Daganzo, 2005a,b), the variational principle was applied to solve (2) analytically and numerically.”
Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model (2011, methodology): “Triangular fundamental diagrams are of great importance and relevance for modeling and control applications, see (Daganzo, 2005a; Daganzo, 1994) for instance.”
An analytical approximation for the macropscopic fundamental diagram of urban traffic (2008, methodology): “It has been shown (Daganzo, 2005b) that for linear CF’s an optimal path always exists that is piece-wise linear: either following an intersection line or else slanting up or down with slope uf or –w.”