Traffic Flow on Networks

By Mauro Garavello, Benedetto Piccoli. 2006

406 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/911d1b22dd990a954c040bd5f0e345cdc8cb3d68

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Citations in the corpus

Continuous formulations and analytical properties of the link transmission model (2014, methodology): “ the initialization, propagation, and dissipation of vehicular queues on a road link through shock and rarefaction waves, has been extended as network kinematic wave models (Holden and Risebro, 1995; Garavello and Piccoli, 2006), by incorporating macroscopic merging, diverging, and junction models, ”
Hamilton–Jacobi equations constrained on networks (2012, background): “But in the recent years there is an increasing interest in the investigation of dynamical systems and diﬀerential equation on networks, in particular in connection with problem of data transmission and traﬃc management (see for example Garavello-Piccoli [9], Engel et al [6]).”
A traffic model for velocity data assimilation (2010, methodology): “This extension is addressed in the literature for density traffic models in the transportation engineering community using physical principles in [7], and also in a mathematical context in [11].”
A Hamilton-Jacobi approach to junction problems and application to traffic flows (2011, unknown): “In particular, we recover the well-known junction conditions of Lebacque (see [22]) or equivalently those for the Riemann solver at the junction as in the book of Garavello and Piccoli [18]; see also [19].”
A partial differential equation formulation of Vickrey’s bottleneck model, part I: Methodology and theoretical analysis (2013, background): “A list of selected references includes Bressan and Han (2011a,b); Claudel and Bayen (2010a,b); Daganzo (1994, 1995, 2005); Garavello and Piccoli (2006); Han et al. (submitted for publication); Newell (1993).”
Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model (2011, background): “…can be written as N c (i) ini (x, t) = tQ(ki)− kix+ bi : xi + tQ′(ki) ≤ x ≤ xi+1 + tQ′(ki) tR(x−xit )− kixi + bi : xi + tw ≤ x ≤ xi + tQ ′(ki) tR(x−xi+1t )− kixi+1 + bi : xi+1 + tQ ′(ki) ≤ x ≤ xi+1 + tvf (21) k c (i) ini (x, t) = − ∂N c (i) ini ∂x (x, t) = ki : xi + tQ ′(ki) ≤ x ≤ xi+1 +…”
Conservation laws on complex networks (2009, methodology): “Since solutions to Riemann problems are given, we are able to construct piecewise constant approximations via wave-front tracking algorithm; see [9] for the general theory and [24] in the case of networks.”