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We develop backstepping state feedback control to stabilize a moving shockwave in a freeway segment under bilateral boundary actuations of traffic flow. A moving shockwave, consisting of light traffic upstream of the shockwave and heavy…

Optimization and Control · Mathematics 2019-04-10 Huan Yu , Mamadou Diagne , Liguo Zhang , Miroslav Krstic

The Macroscopic Fundamental Diagram is a popular tool used to describe traffic dynamics in an aggregated way, with applications ranging from traffic control to incident analysis. However, estimating the MFD for a given network requires…

Machine Learning · Computer Science 2026-05-12 Amalie Roark , Serio Agriesti , Francisco Camara Pereira , Guido Cantelmo

This paper develops boundary control for freeway traffic with a downstream bottleneck. Traffic on a freeway segment with capacity drop at outlet of the segment is a common phenomenon leading to traffic bottleneck problem. The capacity drop…

Optimization and Control · Mathematics 2019-04-10 Huan Yu , Shumon Koga , Tiago Roux Oliveira , Miroslav Krstic

Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models have been extensively used to describe the anomalous transport…

Numerical Analysis · Mathematics 2022-02-01 Xiao Xu , Marta D'Elia , Christian Glusa , John T. Foster

Existing methods for traffic signal design are either too simplistic to capture realistic traffic characteristics or too complicated to be mathematically tractable. In this study, we attempts to fill the gap by presenting a new method based…

Dynamical Systems · Mathematics 2015-10-06 Wen-Long Jin , Yifeng Yu

We study the derivation of macroscopic traffic models out of optimal speed and follow-the-leader particle dynamics as hydrodynamic limits of non-local Povzner-type kinetic equations. As a first step, we show that optimal speed vehicle…

Statistical Mechanics · Physics 2023-03-13 Felisia Angela Chiarello , Andrea Tosin

This paper analyzes the time-dependent relationship between the mean and variance of travel time on a single corridor under rush hour like congestion patterns. To model this phenomenon, we apply the LWR ((Lighthill & Whitham, 1955),…

Physics and Society · Physics 2025-08-28 Alexander Hammerl , Ravi Seshadri , Thomas Kjær Rasmussen , Otto Anker Nielsen

In this article, we investigate theoretical and numerical properties of the first-order Lighthill-Whitham-Richards (LWR) traffic flow model with time delay. Since standard results from the literature are not directly applicable to the…

Numerical Analysis · Mathematics 2020-03-30 Simone Göttlich , Elisa Iacomini , Thomas Jung

In this paper we extend the Aw-Rascle-Zhang (ARZ) non-equilibrium traffic flow model to take into account the look-ahead capability of connected and autonomous vehicles (CAVs), and the mixed flow dynamics of human driven and autonomous…

Analysis of PDEs · Mathematics 2024-12-09 Shouwei Hui , Michael Zhang

In this paper, we aim at developing new methods to join machine learning techniques and macroscopic differential models for vehicular traffic estimation and forecast. It is well known that data-driven and model-driven approaches have…

Machine Learning · Computer Science 2024-12-06 Maya Briani , Emiliano Cristiani , Elia Onofri

Space-time visualizations of macroscopic or microscopic traffic variables is a qualitative tool used by traffic engineers to understand and analyze different aspects of road traffic dynamics. We present a deep learning method to learn the…

Machine Learning · Computer Science 2022-04-12 Bilal Thonnam Thodi , Zaid Saeed Khan , Saif Eddin Jabari , Monica Menendez

This paper uses supervised learning, random search and deep reinforcement learning (DRL) methods to control large signalized intersection networks. The traffic model is Cellular Automaton rule 184, which has been shown to be a…

Artificial Intelligence · Computer Science 2025-04-07 Jorge A. Laval , Hao Zhou

We propose a kinematic wave-based Deep Convolutional Neural Network (Deep CNN) to estimate high-resolution traffic speed fields from sparse probe vehicle trajectories. We introduce two key approaches that allow us to incorporate kinematic…

Machine Learning · Computer Science 2022-04-12 Bilal Thonnam Thodi , Zaid Saeed Khan , Saif Eddin Jabari , Monica Menendez

We present a network formulation for a traffic flow model with nonlocal velocity in the flux function. The modeling framework includes suitable coupling conditions at intersections to either ensure maximum flux or distribution parameters.…

Numerical Analysis · Mathematics 2022-09-08 Jan Friedrich , Simone Göttlich , Maximilian Osztfalk

Although traffic is one of the massively collected data, it is often only available for specific regions. One concern is that, although there are studies that give good results for these data, the data from these regions may not be…

Machine Learning · Computer Science 2023-10-05 Sarah Almeida Carneiro , Giovanni Chierchia , Jean Charléty , Aurélie Chataignon , Laurent Najman

Traditionally, the Lighthill-Whitham-Richards (LWR) models for homogeneous and inhomogeneous roads have been analyzed in flux-density space with the fundamental diagram of the flux-density relation. In this paper, we present a new framework…

Analysis of PDEs · Mathematics 2010-05-26 Wen-Long Jin , Liang Chen , Elbridge Gerry Puckett

In this paper, we simultaneously address the problems of energy optimal and safe motion planning of electric vehicles (EVs) in a data-driven robust optimization framework. Safe maneuvers, especially in urban traffic, are characterized by…

Systems and Control · Electrical Eng. & Systems 2025-09-09 Simran Kumari , Ashish R. Hota , Siddhartha Mukhopadhyay

This paper aims to predict the traffic flow at one road segment based on nearby traffic volume and weather conditions. Our team also discover the impact of weather conditions and nearby traffic volume on the traffic flow at a target point.…

Machine Learning · Computer Science 2023-11-15 Anh Thi-Hoang Nguyen , Dung Ha Nguyen , Trong-Hop Do

Deep learning (DL) models for spatio-temporal traffic flow forecasting employ convolutional or graph-convolutional filters along with recurrent neural networks to capture spatial and temporal dependencies in traffic data. These models, such…

Machine Learning · Computer Science 2023-07-18 Agnimitra Sengupta , S. Ilgin Guler

This paper studies the problem of traffic flow forecasting, which aims to predict future traffic conditions on the basis of road networks and traffic conditions in the past. The problem is typically solved by modeling complex…

Machine Learning · Computer Science 2023-09-22 Yusheng Zhao , Xiao Luo , Wei Ju , Chong Chen , Xian-Sheng Hua , Ming Zhang