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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

Autonomous vehicles are expected to navigate in complex traffic scenarios with multiple surrounding vehicles. The correlations between road users vary over time, the degree of which, in theory, could be infinitely large, thus posing a great…

Robotics · Computer Science 2019-10-24 Yaohui Guo , Vinay Varma Kalidindi , Mansur Arief , Wenshuo Wang , Jiacheng Zhu , Huei Peng , Ding Zhao

This paper addresses the challenge of ensuring realistic traffic conditions by proposing a methodology that systematically identifies traffic simulation requirements. Using a structured approach based on sub-goals in each study phase,…

Software Engineering · Computer Science 2025-10-17 Sven Tarlowski , Lutz Eckstein

Automated Driving Functions (ADFs) need to comply with spatial properties of varied complexity while driving on public roads. Since such situations are safety-critical in nature, it is necessary to continuously check ADFs for compliance…

Logic in Computer Science · Computer Science 2025-11-19 Ishan Saxena , Bernd Westphal , Martin Fränzle

Modeling processes are the activities of capturing and representing processes and control of their dynamic behavior. Desired features of the model include capture of relevant aspects of a real phenomenon, understandability, and completeness…

Software Engineering · Computer Science 2017-07-28 Sabah Al-Fedaghi , Haya Alahmad

Autonomous driving is an emerging technology that has advanced rapidly over the last decade. Modern transportation is expected to benefit greatly from a wise decision-making framework of autonomous vehicles, including the improvement of…

Artificial Intelligence · Computer Science 2023-12-20 Yuyang Xia , Shuncheng Liu , Quanlin Yu , Liwei Deng , You Zhang , Han Su , Kai Zheng

Avoiding congestion and controlling traffic in urban scenarios is becoming nowadays of paramount importance due to the rapid growth of our cities' population and vehicles. The effective control of urban traffic as a means to mitigate…

Artificial Intelligence · Computer Science 2022-08-08 Matteo Cardellini

We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicles density in the situation of congestion. These models are obtained through asymptotic…

Numerical Analysis · Mathematics 2016-12-13 Florent Berthelin , Thierry Goudon , Bastien Polizzi , Magali Ribot

Advances in vision-based sensors and computer vision algorithms have significantly improved the analysis and understanding of traffic scenarios. To facilitate the use of these improvements for road safety, this survey systematically…

Computer Vision and Pattern Recognition · Computer Science 2026-05-27 Yaoqi Huang , Julie Stephany Berrio , Mao Shan , Stewart Worrall

We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…

Probability · Mathematics 2011-10-24 V. A. Malyshev , A. A. Zamyatin

Autonomous Systems (AS) are increasingly proposed, or used, in Safety Critical (SC) applications. Many such systems make use of sophisticated sensor suites and processing to provide scene understanding which informs the AS' decision-making.…

Systems and Control · Electrical Eng. & Systems 2022-08-19 John Molloy , John McDermid

Autonomous driving systems require robust lane perception capabilities, yet existing vision-based detection methods suffer significant performance degradation when visual sensors provide insufficient cues, such as in occluded or…

Computer Vision and Pattern Recognition · Computer Science 2026-02-03 Yihan Xie , Han Xia , Zhen Yang

This article mediates an mathematical insight to the theory of vehicular headways measured on signalized crossroads. Considering both, mathematical and empirical substances of the socio-physical system studied, we firstly formulate several…

Adaptation and Self-Organizing Systems · Physics 2015-06-19 Milan Krbalek , Jiri Sleis

Validating the safety of Autonomous Vehicles (AVs) operating in open-ended, dynamic environments is challenging as vehicles will eventually encounter safety-critical situations for which there is not representative training data. By…

Artificial Intelligence · Computer Science 2024-03-14 Enrik Maci , Rhys Howard , Lars Kunze

Graph signal processing (GSP) is a framework to analyze and process graph-structured data. Many research works focus on developing tools such as Graph Fourier transforms (GFT), filters, and neural network models to handle graph signals.…

Signal Processing · Electrical Eng. & Systems 2023-03-13 Feng Ji , Wee Peng Tay

Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic…

Systems and Control · Electrical Eng. & Systems 2021-06-09 Renátó Besenczi , Norbert Bátfai , Péter Jeszenszky , Roland Major , Fanny Monori , Márton Ispány

Concepts and techniques from statistical physics inspired a new method for traffic prediction. This method is particularly suitable in settings where the only information available is floating car data. We propose a system, based on the…

Probability · Mathematics 2007-05-23 Arnaud De La Fortelle , Jean-Marc Lasgouttes , Cyril Furtlehner

While macroscopic traffic flow models consider traffic as a fluid, microscopic traffic flow models describe the dynamics of individual vehicles. Capturing macroscopic traffic phenomena remains a challenge for microscopic models, especially…

Computational Engineering, Finance, and Science · Computer Science 2023-08-03 Niklas Kolbe , Moritz Berghaus , Eszter Kalló , Michael Herty , Markus Oeser

A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…

Methodology · Statistics 2016-06-09 Mathias Drton , Marloes H. Maathuis

This contribution summarizes and explains various principles from physics which are used for the simulation of traffic flows in large street networks, the modeling of destination, transport mode, and route choice, or the simulation of urban…

Physics and Society · Physics 2015-06-17 Dirk Helbing , Kai Nagel