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We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average…

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

A driving algorithm that aligns with good human driving practices, or at the very least collaborates effectively with human drivers, is crucial for developing safe and efficient autonomous vehicles. In practice, two main approaches are…

Multiagent Systems · Computer Science 2026-02-10 Zhihao Zhang , Keith Redmill , Chengyang Peng , Bowen Weng

We propose here an autonomous traffic signal control model based on analogy with neural networks. In this model, the length of cycle time period of traffic lights at each signal is autonomously adapted. We find a self-organizing collective…

adap-org · Physics 2008-02-03 Toru Ohira

We propose a model-free reinforcement learning method for controlling mixed autonomy traffic in simulated traffic networks with through-traffic-only two-way and four-way intersections. Our method utilizes multi-agent policy decomposition…

Artificial Intelligence · Computer Science 2021-11-09 Zhongxia Yan , Cathy Wu

We derive a conservation law on a network made of two incoming branches and a single outgoing one from a discrete traffic flow model. The continuous model is obtained from the discrete one by letting the number of vehicles tend to infinity…

Analysis of PDEs · Mathematics 2024-09-04 P Cardaliaguet

In this paper, a multi-lane multi-population microscopic model, which presents stop and go waves, is proposed to simulate traffic on a ring-road. Vehicles are divided between human-driven and autonomous vehicles (AV). Control strategies are…

We establish local-in-time existence and uniqueness results for nonlocal conservation laws with a nonlinear mobility, in several space dimensions, under weak assumptions on the kernel, which is assumed to be bounded and of finite total…

Analysis of PDEs · Mathematics 2025-12-16 Antonin Chodron de Courcel

This paper proposes an improved cellular automaton traffic flow model based on the brake light model, which takes into account that the desired time gap of vehicles is remarkably larger than one second. Although the hypothetical steady…

Cellular Automata and Lattice Gases · Physics 2015-03-23 Junfang Tian , Bin Jia , Shoufeng Ma , Chenqiang Zhu , Rui Jiang , YaoXian Ding

We develop a control design for stabilization of traffic flow in congested regime, based on an Aw-Rascle-Zhang-type (ARZ-type) Partial Differential Equation (PDE) model, for traffic consisting of both ACC-equipped (Adaptive Cruise…

Optimization and Control · Mathematics 2018-12-20 Nikolaos Bekiaris-Liberis , Argiris I. Delis

For a foreseeable future, autonomous vehicles (AVs) will operate in traffic together with human-driven vehicles. Their planning and control systems need extensive testing, including early-stage testing in simulations where the interactions…

Robotics · Computer Science 2020-07-21 Ran Tian , Nan Li , Ilya Kolmanovsky , Yildiray Yildiz , Anouck Girard

Although instantaneous interactions are unphysical, a large variety of maximum entropy statistical inference methods match the model-inferred and the empirically-measured equal-time correlation functions. Focusing on collective motion of…

In this paper we study a traffic intersection with vehicle-actuated traffic signal control. Traffic lights stay green until all lanes within a group are emptied. Assuming general renewal arrival processes, we derive exact limiting…

Probability · Mathematics 2014-09-11 Marko Boon , Ivo Adan , Erik Winands , Doug Down

Autonomous vehicles (AVs) hold vast potential to enhance transportation systems by reducing congestion, improving safety, and lowering emissions. AV controls lead to emergent traffic phenomena; one such intriguing phenomenon is traffic…

Systems and Control · Electrical Eng. & Systems 2024-10-14 Sirui Li , Roy Dong , Cathy Wu

This paper presents a new spatial-temporal nonlocal traffic flow model formulated to overcome the boundedness limitations inherent in classical local formulations. The model introduces an adaptive kernel that captures both spatial and…

Numerical Analysis · Mathematics 2026-03-30 Animesh Biswas , Archie Huang , Shaurya Agarwal , Christopher Housholder

We have developed a modified Nagel-Schreckenberg cellular automata model for describing a conflicting vehicular traffic flow at the intersection of two streets. No traffic lights control the traffic flow. The approaching cars to the…

Physics and Society · Physics 2009-11-13 M. Ebrahim Foulaadvand , Sommayeh Belbasi

Traffic congestion remains a significant challenge in modern urban networks. Autonomous driving technologies have emerged as a potential solution. Among traffic control methods, reinforcement learning has shown superior performance over…

Machine Learning · Computer Science 2025-07-29 Songyang Liu , Muyang Fan , Weizi Li , Jing Du , Shuai Li

We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general…

Analysis of PDEs · Mathematics 2021-08-12 Emanuela Radici , Federico Stra

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

Highway vehicular traffic is an inherently multi-agent problem. Traffic jams can appear and disappear mysteriously. We develop a method for traffic flow control that is applied at the vehicular level via mean-field games. We begin this work…

Optimization and Control · Mathematics 2023-06-06 Amoolya Tirumalai , John S. Baras

The erratic nature of human driving tends to trigger undesired waves that amplify as successive driver reactions propagate from the errant vehicle to vehicles upstream. Known as phantom jams, this phenomenon has been identified in the…

Systems and Control · Electrical Eng. & Systems 2020-08-19 Yujie Li , Sikai Chen , Paul Young Joun Ha , Jiqian Dong , Aaron Steinfeld , Samuel Labi
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