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A recently introduced cellular automaton model for the description of traffic flow is investigated. It generalises asymmetric exclusion models which have attracted a lot of interest in the past. We calculate the so-called fundamental…

Condensed Matter · Physics 2009-10-22 A. Schadschneider , M. Schreckenberg

Due to the complexity of the traffic flow dynamics in urban road networks, most quantitative descriptions of city traffic so far are based on computer simulations. This contribution pursues a macroscopic (fluid-dynamic) simulation approach,…

Fluid Dynamics · Physics 2015-03-18 Amin Mazloumian , Nikolas Geroliminis , Dirk Helbing

We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle…

Condensed Matter · Physics 2009-10-22 Satoshi Yukawa , Macoto Kikuchi

The cellular automata (CA) approach to traffic modeling is extended to allow for spatially homogeneous steady state solutions that cover a two dimensional region in the flow-density plane. Hence these models fulfill a basic postulate of a…

Statistical Mechanics · Physics 2009-11-07 Boris S. Kerner , Sergey L. Klenov , Dietrich E. Wolf

A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…

Other Condensed Matter · Physics 2009-11-10 K. Thomas Waldeer

In this paper, we present a class of systems of non-local conservation laws in one space-dimension incorporating time delay, which can be used to investigate the interaction between autonomous and human-driven vehicles, each characterized…

Analysis of PDEs · Mathematics 2025-01-17 Ilaria Ciaramaglia , Paola Goatin , Gabriella Puppo

Phase-transition models are an important family of non-equilibrium continuum traffic flow models, offering properties like replicating complex traffic phenomena, maintaining anisotropy, and promising potentials for accommodating automated…

Numerical Analysis · Mathematics 2025-07-01 Shaoshuai Chu , Alexander Kurganov , Saeed Mohammadian , Zuduo Zheng

In this paper, we investigate a nonlocal traffic flow model based on a scalar conservation law, where a stochastic velocity function is assumed. In addition to the modeling, theoretical properties of the stochastic nonlocal model are…

Numerical Analysis · Mathematics 2024-07-04 Timo Böhme , Simone Göttlich , Andreas Neuenkirch

Platooning of connected and autonomous vehicles (CAVs) has a significant potential for throughput improvement. However, the interaction between CAVs and non-CAVs may limit the practically attainable improvement due to platooning. To better…

Optimization and Control · Mathematics 2020-11-16 Li Jin , Mladen Cicic , Karl H. Johansson , Saurabh Amin

Traffic models based on cellular automata have high computational efficiency because of their simplicity in describing unrealistic vehicular behavior and the versatility of cellular automata to be implemented on parallel processing. On the…

Multiagent Systems · Computer Science 2013-02-05 Emanuele Rodaro , Öznur Yeldan

This paper presents scalable traffic stability analysis for both pure autonomous vehicle (AV) traffic and mixed traffic based on continuum traffic flow models. Human vehicles are modeled by a non-equilibrium traffic flow model, i.e.,…

Optimization and Control · Mathematics 2024-09-23 Kuang Huang , Xuan Di , Qiang Du , Xi Chen

From the macroscopic viewpoint for describing the acceleration behavior of drivers, this letter presents a weighted probabilistic cellular automaton model (the WP model, for short) by introducing a kind of random acceleration probabilistic…

Physics and Society · Physics 2009-11-13 X. L. Li , H. Kuang , T. Song , S. Q. Dai , Z. P. Li

The volume and types of traffic data in mobile cellular networks have been increasing continuously. Meanwhile, traffic data change dynamically in several dimensions such as time and space. Thus, traffic modeling is essential for theoretical…

Networking and Internet Architecture · Computer Science 2017-04-03 Shuo Wang , Xing Zhang , Jiaxin Zhang , Jian Feng , Wenbo Wang , Ke Xin

With the high frequency of highway accidents,studying how to use connected automated vehicle (CAV) to improve traffic efficiency and safety will become an important issue. In order to investigate how CAV can use the connected information…

Physics and Society · Physics 2023-08-07 Jiali Peng , Wei Shangguan , Linguo Chai , Rui Luo , Ke Gao

Based on experimental traffic data obtained from German and US highways, we propose a novel two-dimensional first-order macroscopic traffic flow model. The goal is to reproduce a detailed description of traffic dynamics for the real road…

Physics and Society · Physics 2017-11-10 Michael Herty , Adrian Fazekas , Giuseppe Visconti

Vehicle-to-vehicle communications can change the driving behavior of drivers significantly by providing them rich information on downstream traffic flow conditions. This study seeks to model the varying car-following behaviors involving…

Systems and Control · Computer Science 2018-09-18 Lin Liu , Chunyuan Li , Yongfu Li , Srinivas Peeta , Lei Lin

A macroscopic model-based approach for estimation of the traffic state, specifically of the (total) density and flow of vehicles, is developed for the case of "mixed" traffic, i.e., traffic comprising both ordinary and connected vehicles.…

Optimization and Control · Mathematics 2015-04-28 Nikolaos Bekiaris-Liberis , Claudio Roncoli , Markos Papageorgiou

In this work we present a nonlocal conservation law with a velocity depending on an integral term over a part of the space. The model class covers already existing models in literature, but it is also able to describe new dynamics mainly…

Analysis of PDEs · Mathematics 2023-04-25 Jan Friedrich , Simone Göttlich , Alexander Keimer , Lukas Pflug

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

In this study, we provide a novel approach for modelling the mixed traffic flow. The basic idea is to integrate models for nonmotorized vehicles (nm-vehicles) with models for motorized vehicles (m-vehicles). Based on the idea, a model for…

Physics and Society · Physics 2007-07-10 X. M. Zhao , B. Jia , Z. Y. Gao