Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions

Calvo, Juan; Nieto, Juan J.; Zagour, Mohamed

doi:10.3390/sym11091093

Cited by 7 publications

(2 citation statements)

References 21 publications

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“…For more information on modeling, analysis and interpretation of the traffic models, including 'car-following models, continuum models, gas kinetic models, fluid-dynamic models, cellular automaton models, AI models and lattice hydrodynamic models', we point the reader to . Additionally, within a multiscale vision, researchers delve into integrated approaches [26][27][28][29] that bridge these different scales to provide a comprehensive understanding of traffic dynamics.…”

Section: Introductionmentioning

confidence: 99%

Impact of driver prediction with density deviation and anticipation in lattice hydrodynamic model with passing

Mehta,

Redhu

2024

Phys. Scr.

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This paper presents an integral lattice hydrodynamic model to examine theimpact of driver’s anticipation, driving prediction with density deviation ofleading vehicle and considering the passing behavior. Both linear and non-linear investigations have been used to obtain the stability condition and“modified Korteweg-de Vries (mKdV)” equation, respectively. The linearstability condition shows that the stable region can be increased by decreas-ing the coefficient of predicted density deviation. Additionally, the stableregion expands with a positive value of driver anticipation but contracts witha negative value. The mKdV equation describe the propagating behavior oftraffic density wave near the critical points. In comparison of the Nagataniand Redhu models, it is observed that for fixed value of density deviationcoefficient, this new model conveys a greater stability zone. To verify thetheoretical findings, “numerical simulation” has been conducted to examinethe traffic flow evolves in the presence of a small disturbances. The ana-lytical results have been discussed for different passing rate with fixed valueof driver’s anticipation α and different values of density deviation coefficientβ. Furthermore, it has been noted that the stable region decreases for allpassing rates when a driver becomes more aware of the average speed ofany neighbouring vehicles. The obtained results in this paper show that thetraffic behavior with the existing model is more realistic. Additionally, thismodel effectively boosts vehicle movement efficiency, reducing congestion andenhances road safety

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Section: Introductionmentioning

confidence: 99%

Impact of driver prediction with density deviation and anticipation in lattice hydrodynamic model with passing

Mehta,

Redhu

2024

Phys. Scr.

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“…An interesting contribution to our special issue has been delivered in [36] for models where the microscopic state includes, in addition to position and velocity, also an additional variable deemed to describe the quality of the driver-vehicle micro-system. An additional novelty of this paper is that both short-range and mean field interactions are introduced to depict velocity changes related to passing phenomena in view of modeling the role of toll gates or traffic highlights.…”

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confidence: 99%

Special Issue “Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems”—Editorial and Research Perspectives

Bellomo

Knopoff

Terna³

2020

Symmetry

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This editorial paper presents a special issue devoted to the development of mathematical tools from kinetic and swarms theory to the modeling and simulations of the dynamics of living systems constituted by very many interacting living entities. Applications refer to several fields: collective learning, behavioral economy, multicellular systems, vehicular traffic, and human crowds. A forward look to research perspectives is focused on the conceptual links between swarms methods and the kinetic theory approach.

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Multiscale derivation of deterministic and stochastic cross-diffusion models in a fluid: A review

Bendahmane,

Karami,

Zagour

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper presents a survey and critical analysis of the mathematical literature on modeling of dynamic populations living in a fluid medium. The present review paper is divided into two main parts: The first part deals with the multiscale derivation of deterministic and stochastic cross-diffusion systems governed by the incompressible Navier–Stokes equations. The derivation is obtained from the underlying description at the microscopic scale in kinetic theory models according to the micro–macro decomposition method. In the second part of this review, we are delighted to present a new variety of mathematical models describing different applications, namely, the pursuit–evasion dynamics, cancer invasion, and virus dynamics. Finally, critical analysis and future research perspectives are discussed.

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Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions

Cited by 7 publications

References 21 publications

Impact of driver prediction with density deviation and anticipation in lattice hydrodynamic model with passing

Impact of driver prediction with density deviation and anticipation in lattice hydrodynamic model with passing

Special Issue “Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems”—Editorial and Research Perspectives

Multiscale derivation of deterministic and stochastic cross-diffusion models in a fluid: A review

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