A variational formulation of kinematic waves: basic theory and complex boundary conditions

By Carlos F. Daganzo. 2005

389 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Safety, Risk, Reliability and Quality, Transportation

View Paper: https://www.semanticscholar.org/paper/283e06af0d39b546277923c8113fe68896553550

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In Control and Systems Engineering

In Safety, Risk, Reliability and Quality

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Citations in the corpus

Three new models for the flow–density relationship: derivation and testing for freeway and urban data (2012, background): “More recently, the role of the concavity condition within the framework of a variational theory of traffic flow has been more precisely described in Daganzo ( 2005 ).”
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.”
On the continuum approximation of the on-and-off signal control on dynamic traffic networks (2013, methodology): “As part of our contribution in methodology, we invoke the analytical framework of variational theory (Claudel and Bayen, 2010a; Daganzo, 2005; Newell, 1993) and weak value conditions (Aubin et al., 2008) to analyze the models of interest.”
An analytical approximation for the macropscopic fundamental diagram of urban traffic (2008, methodology): “It has been recently proposed (Daganzo, 2005, 2007) that traffic can be modeled dynamically in large urban regions (neighborhoods) at an aggregate level if the neighborhoods are uniformly congested and flows on their individual links exhibit fundamental diagrams (FD).”
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.”
A mechanism to describe the formation and propagation of stop-and-go waves in congested freeway traffic (2010, background): “Del Castillo (2001) and Kim & Zhang (2008) took Newell’s conjectures, supposed that the paths between the two congested branches were random and showed how this produces oscillations that grow or dissipate.”
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.”
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.”
A partial differential equation formulation of Vickrey’s bottleneck model, part I: Methodology and theoretical analysis (2013, methodology): “The key component of our methodology is the variational method for Hamilton-Jacobi equations known as the Lax-Hopf formula, see Bressan and Han (2011a); Daganzo (2005); Evans (2010); Le Floch (1988); Lax (1957).”
A robust optimization approach for dynamic traffic signal control with emission considerations (2012, methodology): “It employs a Newell-type variational argument (Newell, 1993; Daganzo, 2005) to capture shock waves and vehicle spillback.”