Hydrodynamic models of traffic flow: Drivers' behaviour and nonlinear diffusion

Bonzani, Ida

doi:10.1016/s0895-7177(00)00042-x

Cited by 38 publications

(13 citation statements)

References 7 publications

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“…Historically, models of group motion where particles adapt to their environment by means of an inner steering mechanism have been developed in the context of traffic modelling. For an overiew of such models we refer to [33]. In the context of biological systems, inner states have been considered in order to model the emergence of coherent behavior in groups of fireflies [34,35].…”

Section: Introductionmentioning

confidence: 99%

Emergence of coherent motion in aggregates of motile coupled maps

Ros

Antonopoulos

Basios

2011

Chaos, Solitons & Fractals

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In this paper we study the emergence of coherence in collective motion described by a system of interacting motiles endowed with an inner, adaptative, steering mechanism. By means of a nonlinear parametric coupling, the system elements are able to swing along the route to chaos. Thereby, each motile can display different types of behavior, i.e. from ordered to fully erratic motion, accordingly with its surrounding conditions. The appearance of patterns of collective motion is shown to be related to the emergence of interparticle synchronization and the degree of coherence of motion is quantified by means of a graph representation.The effects related to the density of particles and to interparticle distances are explored. It is shown that the higher degrees of coherence and group cohesion are attained when the system elements display a combination of ordered and chaotic behaviors, which emerges from a collective self-organization process.

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Section: Introductionmentioning

confidence: 99%

Emergence of coherent motion in aggregates of motile coupled maps

Ros

Antonopoulos

Basios

2011

Chaos, Solitons & Fractals

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“…Now the proof that φ i,J ≥ 0 is clear from (51), and the upper bound φ n+1 J ∈ D φ max follows exactly as in the proof above for an interior point.…”

Section: Theorem 32 Consider Scheme 4 Defined Bymentioning

confidence: 83%

“…These gradient-type terms either emerge from simplified versions of additional balance equations, as in sedimentation models, where they reflect sediment compressibility [7]; accrue from truncated expansions of velocities with displaced arguments reflecting anticipation length, reaction time, and relaxation to equilibrium in traffic modelling [14,45,48]; or are postulated a priori as a formal generaliza- [49][50][51][52]. In traffic modelling, the last assumption has the behaviouristic interpretation that drivers are not only sensitive to the local density, but to the gradient of density.…”

Section: Limitations Of Kinematic Modelsmentioning

confidence: 99%

A family of numerical schemes for kinematic flows with discontinuous flux

et al. 2007

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Multiphase flows of suspensions and emulsions are frequently approximated by spatially one-dimensional kinematic models, in which the velocity of each species of the disperse phase is an explicitly given function of the vector of concentrations of all species. The continuity equations for all species then form a system of conservation laws which describes spatial segregation and the creation of areas of different composition. This class of models also includes multi-class traffic flow, where vehicles belong to different classes according to their preferential velocities. Recently, these models were extended to fluxes that depend discontinuously on the spatial coordinate, which appear in clarifier-thickener models, in duct flows with abruptly varying cross-sectional area, and in traffic flow with variable road surface conditions. This paper presents a new family of numerical schemes for such kinematic flows with a discontinuous flux. It is shown how a very simple scheme for the scalar case, which is adapted to the "concentration times velocity" structure of the flux, can be extended to kinematic models with phase velocities that change sign, flows with two or more species (the system case), and discontinuous fluxes. In addition, a MUSCL-type upgrade in combination with a Runge-Kutta-type time discretization can be devised to attain second-order accuracy. It is proved that two particular schemes within the family, which apply to systems of conservation laws, preserve an invariant region of admissible concentration vectors, provided that all velocities have the same sign. Moreover, for the relevant case of a multiplicative flux discontinuity and a constant maximum density, it is proved that one scalar version converges to a BV t entropy solution of the model. In the latter case, the compactness proof involves -R. Bürger et al. a novel uniform but local estimate of the spatial total variation of the approximate solutions. Numerical examples illustrate the performance of all variants within the new family of schemes, including applications to problems of sedimentation, traffic flow, and the settling of oil-in-water emulsions.

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“…The principle is inspired by hydrofluid dynamics and has been retranscribed by analogy to a flow of vehicles and a road network [1]. The simulation of traffic evolution consists of the evaluation of these equations.…”

Section: Generation Of Traffic Flowmentioning

confidence: 99%

AReViRoad: a virtual reality tool for traffic simulation

Herviou¹,

Maisel²

2006

WIT Transactions on the Built Environment, Vol 89

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In this article we introduce AReViRoad, a virtual reality tool: a traffic road simulator that enables one to determine the impact of the road network on traffic fluidity. The traffic generation is based on a multi-agent system in which each vehicle (an entity) is a software agent with its own behavior (autonomous). This solution offers a credible traffic road that will be used for testing a road network. With a set of given tools one can create one's own road network. Thereafter, one can configure one's own simulation (number of vehicles, tested road network, flow of car generators) and then launch, observe and analyse it with dedicated tools, such as a 3D view, flow meter and timer.

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Hydrodynamic models of traffic flow: Drivers' behaviour and nonlinear diffusion

Cited by 38 publications

References 7 publications

Emergence of coherent motion in aggregates of motile coupled maps

Emergence of coherent motion in aggregates of motile coupled maps

A family of numerical schemes for kinematic flows with discontinuous flux

AReViRoad: a virtual reality tool for traffic simulation

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