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We study the spatiotemporal patterns resulting from different boundary conditions for a microscopic traffic model and contrast it with empirical results. By evaluating the time series of local measurements, the local traffic states are…

Physics and Society · Physics 2013-07-08 Florian Knorr , Michael Schreckenberg

In this article an anisotropic interaction model avoiding collisions is proposed. Starting point is a general isotropic interacting particle system, as used for swarming or follower-leader dynamics. An anisotropy is induced by rotation of…

Analysis of PDEs · Mathematics 2020-08-17 Claudia Totzeck

This work presents a novel framework for the formation control of multiple autonomous ground vehicles in an on-road environment. Unique challenges of this problem lie in 1) the design of collision avoidance strategies with obstacles and…

Robotics · Computer Science 2016-05-03 Xiangjun Qian , Florent Altché , Arnaud de La Fortelle , Fabien Moutarde

The goal of this paper is to derive rigorously macroscopic traffic flow models from microscopic models. More precisely, for the microscopic models, we consider follow-the-leader type models with different types of drivers and vehicles which…

Analysis of PDEs · Mathematics 2019-07-05 Pierre Cardaliaguet , Nicolas Forcadel

Recent transportation research highlights the potential of autonomous vehicles (AV) to improve traffic flow mobility as they are able to maintain smaller car-following distances. However, as a unique class of ground robots, AVs are…

Robotics · Computer Science 2025-07-09 Hangyu Li , Xiaotong Sun , Chenglin Zhuang , Xiaopeng Li

Connections between microscopic follow-the-leader and macroscopic fluid-dynamics traffic flow models are already well understood in the case of vehicles moving on a single road. Analogous connections in the case of road networks are instead…

Dynamical Systems · Mathematics 2016-10-04 Emiliano Cristiani , Smita Sahu

In this work, we propose a learning based neural model that provides both the longitudinal and lateral control commands to simultaneously navigate multiple vehicles. The goal is to ensure that each vehicle reaches a desired target state…

Robotics · Computer Science 2024-03-22 Yining Ma , Qadeer Khan , Daniel Cremers

This paper examines the optimal velocity follow-the-leader dynamics, a microscopic traffic model, and explores different aspects of the dynamical model, with particular emphasis on collision analysis. More precisely, we present a rigorous…

Optimization and Control · Mathematics 2023-09-22 Hossein Nick Zinat Matin , Maria Laura Delle Monache

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

Facing the congestion challenges of mixed road networks comprising expressways and arterial road networks, traditional control solutions fall short. To effectively alleviate traffic congestion in mixed road networks, it is crucial to clear…

Systems and Control · Electrical Eng. & Systems 2024-05-13 Yunran Di , Haotian Shi , Weihua Zhang , Heng Ding , Xiaoyan Zheng , Bin Ran

Using the standard Vicsek model, I show how the macroscopic transport equations can be systematically derived from microscopic collision rules. The approach starts with the exact evolution equation for the N-particle probability…

Statistical Mechanics · Physics 2017-05-22 Thomas Ihle

We present a macroscopic traffic flow model where standard vehicles coexist with vehicles informed on the traffic distribution. The resulting mixed nonlocal-local integro-differential PDEs is proved to generate a locally Lipschitz…

Analysis of PDEs · Mathematics 2025-11-03 Rinaldo M. Colombo , Mauro Garavello , Claudia Nocita

Classical second order models of pedestrian dynamics, like the social-force model, suffer from various unrealistic behaviors in the dynamics, e.g. backward motion, oscillations and overlapping of pedestrians. These effects are not related…

Physics and Society · Physics 2019-11-19 Jakob Cordes , Andreas Schadschneider , Antoine Tordeux

The paper provides results for a non-standard, hyperbolic, 1-D, nonlinear traffic flow model on a bounded domain. The model consists of two first-order PDEs with a dynamic boundary condition that involves the time derivative of the…

Optimization and Control · Mathematics 2017-07-10 Iasson Karafyllis , Nikolaos Bekiaris-Liberis , Markos Papageorgiou

We consider the problem of incentivization and optimal control of autonomous vehicles for improving traffic congestion. In our scenario, autonomous vehicles must be incentivized in order to participate in traffic improvement. Using the…

Optimization and Control · Mathematics 2020-06-18 Uroš Kalabić , Piyush Grover , Shuchin Aeron

An urban traffic system is a heterogeneous system, which consists of different types of intersections and dynamics. In this paper, we focus on one type of heterogeneous traffic network, which consists of signalized junctions and…

Optimization and Control · Mathematics 2017-05-11 Yicheng Zhang , Rong Su , Yi Zhang , Chunyang Sun

Connected and Automated Vehicles (CAVs) offer significant potential for improving energy efficiency and lowering vehicle emissions through eco-driving technologies. Control algorithms in CAVs leverage look-ahead route information and…

Systems and Control · Electrical Eng. & Systems 2025-10-13 Mehmet Fatih Ozkan , Dennis Kibalama , Jacob Paugh , Marcello Canova , Stephanie Stockar

With the rapid growth of urban transportation and the continuous progress in autonomous driving, a demand for robust benchmarking autonomous driving algorithms has emerged, calling for accurate modeling of large-scale urban traffic…

Robotics · Computer Science 2025-02-14 Yuheng Zhang , Tianjian Ouyang , Fudan Yu , Lei Qiao , Wei Wu , Jingtao Ding , Jian Yuan , Yong Li

Active traffic management with autonomous vehicles offers the potential for reduced congestion and improved traffic flow. However, developing effective algorithms for real-world scenarios requires overcoming challenges related to…

Machine Learning · Computer Science 2024-09-04 Shengchao Yan , Lukas König , Wolfram Burgard

Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…

Optimization and Control · Mathematics 2025-07-29 Anqi Dong , Karl Henrik Johansson , Johan Karlsson