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A two parameter model for single lane car-following is introduced and its equilibrium and non-equilibrium properties are studied. Despite its simplicity, this model exhibits a rich phenomenology, analogous to that observed in real traffic,…

Statistical Mechanics · Physics 2007-05-23 M. Antoni , R. Cafiero

Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…

Machine Learning · Computer Science 2026-02-20 Xinghao Dong , Huchen Yang , Jin-long Wu

Traffic congestion is usually observed at the upper streams of bottlenecks such as tunnels. Congestion appears as stop-and-go waves and high density uniform flow. We perform simulations of traffic flow with a bottleneck using the coupled…

Physics and Society · Physics 2007-05-23 Syohei Yamamoto , Yasuhiro Hieida , Shin-ichi Tadaki

Time-dependent fixed-time control is a cost-effective control method that is widely employed at signalized intersections in numerous countries. Existing optimization models rely on traditional delay models with specific assumptions…

Optimization and Control · Mathematics 2024-08-01 Chaopeng Tan , Yumin Cao , Xuegang , Ban , Keshuang Tang

The problem of a car following a lead car driven with constant velocity is considered. To derive the governing equations for the following car dynamics a cost functional that ranks the outcomes of different driving strategies is…

Soft Condensed Matter · Physics 2007-05-23 Ihor Lubashevsky , Peter Wagner , Reinhard Mahnke

While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with…

Statistical Mechanics · Physics 2009-11-10 Dirk Helbing

Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…

Statistics Theory · Mathematics 2025-12-11 Gonzalo Mena , Arun Kumar Kuchibhotla , Larry Wasserman

We consider the follow-the-leader model for traffic flow. The position of each car $z_i(t)$ satisfies an ordinary differential equation, whose speed depends only on the relative position $z_{i+1}(t)$ of the car ahead. Each car perceives a…

Analysis of PDEs · Mathematics 2017-12-20 Wen Shen , Karim Shikh-Khalil

With the aim of providing a first step in the quest for a reduction of the aerodynamic drag on the rear-end of a car, we study the phenomena of separation and reattachment of an incompressible flow focusing on a specific aerodynamic…

Fluid Dynamics · Physics 2019-02-28 Marco Martins Afonso , Philippe Meliga , Eric Serre

We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…

Chaotic Dynamics · Physics 2025-01-22 Thomas Burton , Sean Symon , Ati Sharma , Davide Lasagna

Car-following behavior modeling is critical for understanding traffic flow dynamics and developing high-fidelity microscopic simulation models. Most existing impulse-response car-following models prioritize computational efficiency and…

Applications · Statistics 2025-04-09 Chengyuan Zhang , Wenshuo Wang , Lijun Sun

We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of…

Statistical Mechanics · Physics 2009-11-07 H. K. Lee , H. -W. Lee , D. Kim

A novel continuum model has been developed to address the vehicle size heterogeneity in mixed traffic. By incorporating the principle of vehicle area conservation, a new set of traffic flow variables centered on the concept of vehicle area…

Analysis of PDEs · Mathematics 2026-04-27 Nandan Maiti , Bhargava Rama Chilukuri

In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…

Analysis of PDEs · Mathematics 2019-12-24 Yang Li , Ewelina Zatorska

Widespread development of driverless vehicles has led to the formation of autonomous racing, where technological development is accelerated by the high speeds and competitive environment of motorsport. A particular challenge for an…

Robotics · Computer Science 2021-09-16 Sam Garlick , Andrew Bradley

This paper presents two one-dimensional mathematical models describing automobile traffic flow on straight road segments at a signalized intersection. When the traffic light is permissive, the flow density and velocity are obtained by…

Analysis of PDEs · Mathematics 2026-04-29 Akbota Senkebayeva

Vehicle velocities in neighbouring road sections are correlated with memory effects. We explore the response of the velocities in the sequence of sections to a congestion in a given section and its dynamic characteristics. To this end, we…

Physics and Society · Physics 2023-08-21 Shanshan Wang , Michael Schreckenberg , Thomas Guhr

We focus on entropy admissible solutions of scalar conservation laws in one space dimension and establish new regularity results with respect to time. First, we assume that the flux function $f$ is strictly convex and show that, for every $…

Analysis of PDEs · Mathematics 2021-07-15 Simone Dovetta , Elio Marconi , Laura V. Spinolo

Car-Following is a broadly studied state of driving, and many modeling approaches through various heuristics and engineering methods have been proposed. Congestion is a common traffic phenomenon also widely investigated, both from…

Physics and Society · Physics 2025-11-25 Huaidian Hou , Arpan Kusari , Brian T. W. Lin

Accurate trajectory prediction is fundamental to autonomous driving, as it underpins safe motion planning and collision avoidance in complex environments. However, existing benchmark datasets suffer from a pronounced long-tail distribution…

Robotics · Computer Science 2025-10-06 Ruining Yang , Yi Xu , Yixiao Chen , Yun Fu , Lili Su