• Corpus ID: 220845737

Mean-field limit of a hybrid system for multi-lane multi-class traffic

@article{Gong2020MeanfieldLO,
  title={Mean-field limit of a hybrid system for multi-lane multi-class traffic},
  author={Xiaoqian Gong and Benedetto Piccoli and Giuseppe Visconti},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
This article aims to study coupled mean-field equation and ODEs with discrete events motivated by vehicular traffic flow. Multi-lane traffic flow in presence of human-driven and autonomous vehicles is considered, with the autonomous vehicles possibly influenced by external policy makers. First a finite-dimensional hybrid system is developed based on the continuous Bando-Follow-the-Leader dynamics coupled with discrete events due to lane changing. The mean-field limit of the finite-dimensional… 

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References

SHOWING 1-10 OF 61 REFERENCES
Mean-Field of Optimal Control Problems for Hybrid Model of Multilane Traffic
TLDR
A hybrid system, where the lane-changing mechanism has three components: safety, incentive and cool-down time is designed, consisting of coupled controlled hybrid ODEs and Vlasov-type PDE with source terms representing lane-change.
A rigorous multi-population multi-lane hybrid traffic model and its mean-field limit for dissipation of waves via autonomous vehicles
In this paper, a multi-lane multi-population microscopic model, which presents stop and go waves, is proposed to simulate traffic on a ring-road. Vehicles are divided between human-driven and
Models for Dense Multilane Vehicular Traffic
TLDR
By taking an appropriately scaled limit as the number of lanes increases, a model describing a continuum of lanes is derived, and it is shown that the $N$-lane model converges to a weak solution of the continuum model.
A Second Order Traffic Flow Model with Lane Changing
TLDR
A new second order model is proposed in which the acceleration terms take lead from microscopic car-following models, and yield a nonlinear hyperbolic system with viscous and relaxation terms.
Feedback Control Algorithms for the Dissipation of Traffic Waves with Autonomous Vehicles
TLDR
It is shown that both in simulation and in the field test that an autonomous vehicle is able to dampen waves generated by 22 cars, and that the total fuel consumption of all vehicles is reduced by up to 20%.
Model-based assessment of the impact of driver-assist vehicles using kinetic theory
TLDR
A kinetic description of follow-the-leader traffic models is considered, which suggests that the kinetic approach may be a valid tool for an organic multiscale investigation and possibly design of driver-assist algorithms.
Macroscopic Modeling of Multilane Motorways Using a Two-Dimensional Second-Order Model of Traffic Flow
TLDR
A macroscopic model, which accounts for lane-changing behavior on motorway, based on a two-dimensional extension of the Aw and Rascle-Zhang model, and a detailed analysis of the space-time discretization of the proposed Macroscopic as well as an approximation of the solution to the associated Riemann problem.
Decentralized delayed-feedback control of an optimal velocity traffic model
TLDR
It is shown that -norm, which has been used in the field of control theory, can reveal the traffic jam phenomenon in an optimal velocity traffic model under an open boundary condition and suppress the traffic jams in the model by the decentralized delayed-feedback control method.
Mathematical modeling of vehicular traffic: a discrete kinetic theory approach
TLDR
A discrete velocity mathematical model for vehicular traffic along a one-way road using the kinetic scale to capture the probabilistic essence of the interactions among the vehicles and offers the opportunity of a profitable analytical investigation of the relevant global features of the system.
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