Resurrection of "Second Order" Models of Traffic Flow

By A. Aw, Michel Rascle. SIAM Journal on Applied Mathematics, 2000

1,343 citations recorded by the source corpus.

Subfields: Computational Mechanics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/f1f98f318930dea943b452a5ec70e8db401b06db

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Control and Systems Engineering

Citations in the corpus

Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments (2017, background): “Moreover, these waves can be captured in microscopic models of individual vehicle motion [10, 11, 12] (see also the reviews [13, 14, 15]) and macroscopic models described via solutions to continuum problems [3, 16, 17, 18, 19, 20].”
A new fundamental diagram theory with the individual difference of the driver’s perception ability (2012, methodology): “In order to conquer this drawback, Aw and Rascle [51, 59] proposed the first SG model and Zhang [60] extended it, but the two models did not consider the relaxation term.”
The Aw–Rascle traffic model with locally constrained flow (2010, methodology): “1 Introduction The paper deals with solutions to the Aw-Rascle vehicular traffic model [2]”
Multi-scale Graphical Models for Spatio-Temporal Processes (2014, background): “Other examples of multi-scale spatio-temporal phenomena with the network structure include: flow of information through neural/brain networks [15], traffic flow through traffic networks[3]; spread of memes through social networks [23]; diffusion of salinity, temperature, pressure and pollutants in a”
Traffic Flow on a Road Network (2002, methodology): “In particular some models using systems of two conservation laws have been proposed, see [4, 9, 10].”
Flow: A Modular Learning Framework for Mixed Autonomy Traffic (2017, background): “The low uncertainty in system dynamics permits direct modeling and analysis within a number of powerful mathematical frameworks, including partial differential equations [16], [17], [18], [19], ordinary differential equations [20], [21], [22], [23], and queuing systems [24], [25], [26].”
Source-Destination Flow on a Road Network (2005, methodology): “In particular, [11] is based on a second order model proposed by Aw and Rascle [3] in 2000.”
Traffic Flow on a Road Network Using the Aw–Rascle Model (2006, methodology): “This consists of a hyperbolic system of two equations proposed in Aw and Rascle (2000). A method to solve Riemann problems at junctions is given assigning rules on traffic distributions and maximizations of fluxes and other quantities.”
Conservation laws on complex networks (2009, methodology): “models with two equations, were considered, see for example [1, 13, 24, 26, 35, 37, 40, 41], while a third order model was presented in [27].”
A Model for the Formation and Evolution of Traffic Jams (2008, background): “Recently, Aw and Rascle [2] proposed a new second-order model (in this work referred to as the Aw-Rascle or AR model) which remedies to the deficiencies pointed out by Daganzo.”
On the modelling and management of traffic (2011, methodology): “wave front tracking, as well as the general framework described below, may be easily extended substituting the LWR equation with the 2-phase models [7,10,14,15,19] or also with the classical Aw–Rascle model [5,42].”
Traffic jams: dynamics and control (2010, background): “In response to this criticism N = rP (r)v x v has been proposed by Aw & Rascle (2000), where the function P(r) represents anticipation.”