The Aw–Rascle and Zhang’s model: Vacuum problems, existence and regularity of the solutions of the Riemann problem

Lebacque, Jean-Patrick; Mammar, Salim; Haj-Salem, Habib

doi:10.1016/j.trb.2006.11.005

Cited by 71 publications

(34 citation statements)

References 5 publications

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“…We assume a macroscopic model described in [Sewall et al 2010], based on the equations of Aw and Rascle [2000] and Zhang [2002]. Following Lebacque [2007], we refer to this as the Aw-Rascle-Zhang (ARZ) model. This traffic model describes the evolution of aggregate traffic statistics, density and velocity, along lanes and makes use of a parameter for determining the speedlimit, v max , and a parameter γ to define a relationship between the velocity and the density.…”

Section: State Estimationmentioning

confidence: 99%

Flow reconstruction for data-driven traffic animation

Wilkie¹,

Sewall

Lin³

2013

ACM Trans. Graph.

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Figure 1: The divided highway is populated with vehicle traffic using our flow reconstruction method. Individual virtual cars are animated and correspond to real-world traffic conditions measured by road sensors. The vehicle motions are simulated on a GIS-derived domain and overlaid on a public domain aerial image from the U.S. Geological Survey. Abstract'Virtualized traffic' reconstructs and displays continuous traffic flows from discrete spatio-temporal traffic sensor data or procedurally generated control input to enhance a sense of immersion in a dynamic virtual environment. In this paper, we introduce a fast technique to reconstruct traffic flows from in-road sensor measurements or procedurally generated data for interactive 3D visual applications. Our algorithm estimates the full state of the traffic flow from sparse sensor measurements (or procedural input) using a statistical inference method and a continuum traffic model. This estimated state then drives an agent-based traffic simulator to produce a 3D animation of vehicle traffic that statistically matches the original traffic conditions. Unlike existing traffic simulation and animation techniques, our method produces a full 3D rendering of individual vehicles as part of continuous traffic flows given discrete spatio-temporal sensor measurements. Instead of using a color map to indicate traffic conditions, users could visualize and fly over the reconstructed traffic in real time over a large digital cityscape.

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Section: State Estimationmentioning

confidence: 99%

Flow reconstruction for data-driven traffic animation

Wilkie¹,

Sewall

Lin³

2013

ACM Trans. Graph.

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“…[Lebacque et al 2007] noted that these two models could be unified through a change of variables, and dubbed the system the 'Aw-Rascle-Zhang' (ARZ) system of equations.…”

Section: Related Workmentioning

confidence: 99%

Interactive hybrid simulation of large-scale traffic

Sewall¹,

Wilkie

Dubey³

2011

Proceedings of the 2011 SIGGRAPH Asia Conference

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a) (b) Figure 1: (a) Interactive 3D visualization of urban traffic; (b) Augmenting a satellite earth map of a metropolitan region with real-time moving traffic consisting of tens of thousands of vehicles using our method. AbstractWe present a novel, real-time algorithm for modeling large-scale, realistic traffic using a hybrid model of both continuum and agentbased methods for traffic simulation. We simulate individual vehicles in regions of interest using state-of-the-art agent-based models of driver behavior, and use a faster continuum model of traffic flow in the remainder of the road network. Our key contributions are efficient techniques for the dynamic coupling of discrete vehicle simulation with the aggregated behavior of continuum techniques for traffic simulation. We demonstrate the flexibility and scalability of our interactive visual simulation technique on extensive road networks using both real-world traffic data and synthetic scenarios. These techniques demonstrate the applicability of hybrid techniques to the efficient simulation of large-scale flows with complex dynamics.

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“…Equations (11), (12), and (13) will be used throughout this section, but the expression for the trajectories, χ(m, t), will be different for equilibrium and non-equilibrium models.…”

Section: Lagrangian Coordinatesmentioning

confidence: 99%

“…Macroscopic traffic flow models have gained much attention from researchers in recent years, owing in part to the success of second order models [2,3,9,12,16] which are now largely free of the un-physical features previously exhibited [18], as outlined by Daganzo [5], due to the corrections made by Aw and Rascle [3]. In contrast with first-order, one-equation macroscopic models, these contain a second equation which allow non-equilibrium traffic to be modeled.…”

Section: Introductionmentioning

confidence: 99%

Modeling non-equilibrium traffic dynamics in a Lagrangian framework

Tchrakian

Basu

2011

Nonlinear Dyn

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In this paper, we propose a formulation for modeling macroscopic traffic flow using a modified speed-density relationship. The flow model consists of a nonlinear hyperbolic system of conservation laws. The proposed modification distinguishes between acceleration and deceleration by assuming a different equilibrium velocity for a given traffic density based on whether a platoon of vehicles is accelerating or decelerating. We examine the appropriateness of this modification to two prominent traffic flow models in a Lagrangian reference frame, which we solve computationally. We show that a Lagrangian coordinate system is ideal for the incorporation of the proposed modification due to its ability to track the behavior of moving vehicles. We see that the modification is particularly well suited to "second order" models.

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The Aw–Rascle and Zhang’s model: Vacuum problems, existence and regularity of the solutions of the Riemann problem

Cited by 71 publications

References 5 publications

Flow reconstruction for data-driven traffic animation

Flow reconstruction for data-driven traffic animation

Interactive hybrid simulation of large-scale traffic

Modeling non-equilibrium traffic dynamics in a Lagrangian framework

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