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This contribution investigates an original stochastic approach for the emergence of stop-and-go waves in traffic flow, a collective phenomenon with significant safety and environmental implications. Using a stable nonlinear car-following…

Physics and Society · Physics 2025-12-04 Raphael Korbmacher , Parthib Khound , Antoine Tordeux , Frank Gronwald

On the basis of a lattice gas model and the convolution formula with cell construction scheme, we demonstrate that intermittency in the rapidity-space with respect to the scaled moments comes from a phase transition between ordered phase…

High Energy Physics - Phenomenology · Physics 2007-05-23 E. R. Nakamura , K. Kudo , T. Hashimoto , I. Yoneda

Traffic flow modeling relies heavily on fundamental diagrams. However, deterministic fundamental diagrams, such as single or multi-regime models, cannot capture the uncertainty pattern that underlies traffic flow. To address this…

Applications · Statistics 2024-11-25 Yuan-Zheng Lei , Yaobang Gong , Xianfeng Terry Yang

The traffic flow through a light signal is explored by using the optimal velocity model and its improvement known as full velocity differences model. The simulations consider a single line of identical cars, equally spaced, and with no…

Physics and Society · Physics 2017-12-07 Juan Carlos Cardona

A microscopic theory of control of spatial-temporal congested traffic pattern at freeway bottlenecks is presented. Based on empirical spatial-temporal features of congested patterns at freeway bottlenecks which have recently been found,…

Statistical Mechanics · Physics 2009-11-10 Boris S. Kerner

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

Recently, a phase transition to synchronized congested traffic has been observed in empirical highway data [B. S. Kerner and H. Rehborn, Phys. Rev. Lett. 79, 4030 (1997)]. This hysteretic transition has been described by a non-local,…

Statistical Mechanics · Physics 2009-10-31 Martin Treiber , Dirk Helbing

Traditional planning and control methods could fail to find a feasible trajectory for an autonomous vehicle to execute amongst dense traffic on roads. This is because the obstacle-free volume in spacetime is very small in these scenarios…

Robotics · Computer Science 2022-12-29 Dhruv Mauria Saxena , Sangjae Bae , Alireza Nakhaei , Kikuo Fujimura , Maxim Likhachev

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

In a recent paper (Physica A 296, 320 (2001)), T. Nagatani proposes a time-headway model for buses on a bus route, and studies the stability of that model's homogeneous solutions. While investigating the phase diagram gotten by varying the…

Statistical Mechanics · Physics 2007-05-23 Scott A Hill

In this paper, we propose a stochastic cellular automaton model of traffic flow extending two exactly solvable stochastic models, i.e., the asymmetric simple exclusion process and the zero range process. Moreover it is regarded as a…

Statistical Mechanics · Physics 2009-05-26 Masahiro Kanai , Katsuhiro Nishinari , Tetsuji Tokihiro

Urban rail transit often operates with high service frequencies to serve heavy passenger demand during rush hours. Such operations can be delayed by two types of congestion: train congestion and passenger congestion, both of which interact…

Systems and Control · Computer Science 2025-09-16 Toru Seo , Kentaro Wada , Daisuke Fukuda

Traffic flow prediction is a typical spatio-temporal prediction problem and has a wide range of applications. The core challenge lies in modeling the underlying complex spatio-temporal dependencies. Various methods have been proposed, and…

Machine Learning · Computer Science 2026-01-16 Yiqing Zou , Hanning Yuan , Qianyu Yang , Ziqiang Yuan , Shuliang Wang , Sijie Ruan

We study a model of synthetic molecular motor - a [3]-catenane consisting of two small macrocycles mechanically interlocked with a bigger one - subjected to a time-dependent driving using stochastic thermodynamics. The model presents…

Statistical Mechanics · Physics 2023-06-28 Massimo Bilancioni , Massimiliano Esposito , Emanuele Penocchio

We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic ``particle-hopping'' traffic flow…

Dynamical Systems · Mathematics 2009-11-10 Michael Blank

Calibration and validation techniques are crucial in assessing the descriptive and predictive power of car-following models and their suitability for analyzing traffic flow. Using real and generated floating-car and trajectory data, we…

Physics and Society · Physics 2014-03-21 Martin Treiber , Arne Kesting

At an unmanaged intersection, it is important to understand how much traffic delay may be caused as a result of microscopic vehicle interactions. Conventional traffic simulations that explicitly track these interactions are time-consuming.…

Multiagent Systems · Computer Science 2018-06-08 Changliu Liu , Mykel J. Kochenderfer

From single vehicle data a number of new empirical results concerning the density-dependence of the velocity distribution and its moments as well as the characteristics of their temporal fluctuations have been determined. These are utilized…

Statistical Mechanics · Physics 2009-10-31 Dirk Helbing

We study the effect of reaction times on the kinetics of relaxation to stationary states and on congestion transitions in heterogeneous traffic. Heterogeneity is modeled as quenched disorders in the parameters of the car following model and…

Physics and Society · Physics 2021-03-10 A. Sai Venkata Ramana , Saif Eddin Jabari

We present a macroscopic model of mixed multi-lane freeway traffic that can be easily calibrated to empirical traffic data, as is shown for Dutch highway data. The model is derived from a gas-kinetic level of description, including effects…

Statistical Mechanics · Physics 2009-10-31 Vladimir Shvetsov , Dirk Helbing