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We study a hierarchy of models based on kinetic equations for the descriptions of traffic flow in presence of autonomous and human--driven vehicles. The autonomous cars considered in this paper are thought of as vehicles endowed with some…

Physics and Society · Physics 2021-10-11 M. Herty , G. Puppo , G. Visconti

We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian…

Mathematical Physics · Physics 2014-04-08 Cécile Appert-Rolland , Pierre Degond , Sébastien Motsch

In multi-agent based traffic simulation, agents are always supposed to move following existing instructions, and mechanically and unnaturally imitate human behavior. The human drivers perform acceleration or deceleration irregularly all the…

Multiagent Systems · Computer Science 2021-01-26 Junjie Zhong , Hiromitsu Hattori

A general and psychologically plausible collision avoidance driver model can improve transportation safety significantly. Most computational driver models found in the literature have used control theory methods only, and they are not…

Systems and Control · Electrical Eng. & Systems 2025-10-21 H. Mozaffari , A. Nahvi

In this paper we consider a kinetic description of follow-the-leader traffic models, which we use to study the effect of vehicle-wise driver-assist control strategies at various scales, from that of the local traffic up to that of the…

Adaptation and Self-Organizing Systems · Physics 2020-08-31 Benedetto Piccoli , Andrea Tosin , Mattia Zanella

The complete flow field surrounding a rotating cylinder is calculated by solving the Navier-Stokes equations using the finite difference method. The numerical simulation is performed on a transformed rectilinear grid, with axes representing…

Computational Physics · Physics 2018-10-25 Alan Hsu , Fei Liu

The curvature field is measured from tracer particle trajectories in a two-dimensional fluid flow that exhibits spatiotemporal chaos, and is used to extract the hyperbolic and elliptic points of the flow. These special points are pinned to…

Fluid Dynamics · Physics 2009-11-13 Nicholas T. Ouellette , J. P. Gollub

A bottleneck situation in one-lane traffic-flow is typically modelled with a constant demand of entering cars. However, in practice this demand may depend on the density of cars in the bottleneck. The present paper studies a simple bimodal…

Statistical Mechanics · Physics 2016-11-26 Marko Woelki

The lateral position of vehicles within their lane is a decisive factor for the range of vision of vehicle sensors. This, in turn, is crucial for a vehicle's ability to perceive its environment and gain a high situational awareness by…

Robotics · Computer Science 2024-05-28 Nicole Neis , Juergen Beyerer

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…

Probability · Mathematics 2021-02-11 Michel Mandjes , Jaap Storm

This contribution presents experimental study of two-dimensional pedestrian flow with the aim to capture the pedestrian behaviour within the cluster formed in front of the bottleneck. Two experiments of passing through a room with one…

Physics and Society · Physics 2018-01-08 Marek Bukáček , Pavel Hrabák , Milan Krbálek

Traffic flow at low densities (free traffic) is characterized by a quasi-one-dimensional relation between traffic flow and vehicle density, while no such fundamental diagram exists for `synchronized' congested traffic flow. Instead, a…

Statistical Mechanics · Physics 2009-11-07 Dirk Helbing , Davide Batic , Martin Schoenhof , Martin Treiber

This paper presents a new mathematical model of vehicular traffic, based on the methods of the generalized kinetic theory, in which the space of microscopic states (position and velocity) of the vehicles is genuinely discrete. While in the…

Mathematical Physics · Physics 2013-11-12 Luisa Fermo , Andrea Tosin

In this paper we propose a novel traffic flow model based on understanding the city as a porous media, this is, streets and building-blocks characterizing the urban landscape are seen now as the fluid-phase and the solid-phase of a porous…

Numerical Analysis · Mathematics 2024-12-02 N. Garcia-Chan , L. J. Alvarez-Vazquez , A. Martinez , M. E. Vazquez-Mendez

Fundamental to many transportation network studies, traffic flow models can be used to describe traffic dynamics determined by drivers' car-following, lane-changing, merging, and diverging behaviors. In this study, we develop a…

Dynamical Systems · Mathematics 2013-07-31 Wen-Long Jin

Active traffic management (ATM) is frequently hindered by traditional macroscopic models and rigid empirical thresholds that fail to capture metastable phase precursors, resulting in delayed, reactive interventions. To address this, we…

Physics and Society · Physics 2026-05-25 Haopeng Deng , Fucheng Zheng , Xinhai Xia

In this paper, a synergistic combination of deep reinforcement learning and hierarchical game theory is proposed as a modeling framework for behavioral predictions of drivers in highway driving scenarios. The need for a modeling framework…

Multiagent Systems · Computer Science 2020-03-26 Berat Mert Albaba , Yildiray Yildiz

This article introduces a model for freeway traffic dynamics under stochastic capacity-reducing incidents, and provides insights for freeway incident management by analyzing long-time (stability) properties of the proposed model. Incidents…

Optimization and Control · Mathematics 2017-11-01 Li Jin , Saurabh Amin

The fundamental relationship of traffic flow is empirically estimated by fitting a regression curve to a cloud of observations of traffic variables. Such estimates, however, may suffer from the confounding/endogeneity bias due to omitted…

Econometrics · Economics 2021-04-07 Anupriya , Daniel J. Graham , Daniel Hörcher , Prateek Bansal

We study the relation between the average traffic flow and the vehicle density on road networks that we call 2D-traffic fundamental diagram. We show that this diagram presents mainly four phases. We analyze different cases. First, the case…

Optimization and Control · Mathematics 2013-02-06 Nadir Farhi , Maurice Goursat , Jean-Pierre Quadrat