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The paper introduces a new bidirectional microscopic inviscid Adaptive Cruise Control (ACC) model that uses only spacing information from the preceding and following vehicles in order to select the proper control action to avoid collisions…

Optimization and Control · Mathematics 2021-09-21 Iasson Karafyllis , Dionysis Theodosis , Markos Papageorgiou

The increasing complexity of urban transportation systems, driven by connected and automated vehicles, calls for new modeling paradigms and scalable control strategies. We propose a non-monetary control framework that leverages autonomous…

Computer Science and Game Theory · Computer Science 2026-04-21 Arda Kosay , Yusuf Saltan , Jyun-Jhe Wang , Chung-Wei Lin , Muhammed O. Sayin

Adaptive-Cruise Control (ACC) automatically accelerates or decelerates a vehicle to maintain a selected time gap, to reach a desired velocity, or to prevent a rear-end collision. To this end, the ACC sensors detect and track the vehicle…

Physics and Society · Physics 2007-06-13 Arne Kesting , Martin Treiber , Martin Schönhof , Florian Kranke , Dirk Helbing

This article deals with macroscopic traffic flow models on a road network. More precisely, we consider coupling conditions at junctions for the Aw-Rascle-Zhang second order model consisting of a hyperbolic system of two conservation laws.…

Numerical Analysis · Mathematics 2018-04-23 Oliver Kolb , Guillaume Costeseque , Paola Goatin , Simone Göttlich

We propose and study a nonlocal conservation law modelling traffic flow in the existence of inter-vehicle communication. It is assumed that the nonlocal information travels at a finite speed and the model involves a space-time nonlocal…

Analysis of PDEs · Mathematics 2023-07-06 Qiang Du , Kuang Huang , James Scott , Wen Shen

Traffic congestion has become a nightmare to modern life in metropolitan cities. On average, a driver spending X hours a year stuck in traffic is one of most common sentences we often read regarding traffic congestion. Our aim in this…

Optimization and Control · Mathematics 2021-11-18 Harshvardhan Uppaluru , Hamid Emadi , Hossein Rastgoftar

We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic, taking…

Popular Physics · Physics 2007-05-23 Dirk Helbing , Stefan Lämmer , Jean-Patrick Lebacque

We present simulations of congested traffic in circular and open systems with a non-local, gas-kinetic-based traffic model and a novel car-following model. The model parameters are all intuitive and can be easily calibrated. Micro- and…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing , Ansgar Hennecke , Vladimir Shvetsov , Martin Treiber

An extended multi-class Aw-Rascle (AR) model with pressure term described as a function of area occupancy defined in form of proportional densities is presented. Two vehicle classes that is; cars and motorcycles are considered based on an…

Analysis of PDEs · Mathematics 2024-05-16 Nanyondo Josephine , Henry Kasumba

We discuss a nonlocal version of the Generalized Aw-Rascle-Zhang model, a second-order vehicular traffic model where the empty road velocity is a Lagrangian marker governed by a transport equation. The evolution of the car density is…

Analysis of PDEs · Mathematics 2025-05-16 Elio Marconi , Laura V. Spinolo

This paper develops a unified modeling framework to capture the equilibrium-state interactions among ride-hailing companies, travelers, and traffic of mixed-autonomy transportation networks. Our framework integrates four interrelated…

Systems and Control · Electrical Eng. & Systems 2025-12-12 Jiaxin Hou , Kexin Wang , Ruolin Li , Jong-shi Pang

We investigate the propagation of uncertainties in the Aw-Rascle-Zhang model, which belongs to a class of second order traffic flow models described by a system of nonlinear hyperbolic equations. The stochastic quantities are expanded in…

Numerical Analysis · Mathematics 2021-05-06 Stephan Gerster , Michael Herty , Elisa Iacomini

Firstly, a new state feedback model reference adaptive control approach is developed for uncertain systems with gain scheduled reference models in a multi-input multi-output (MIMO) setting. Specifically, adaptive state feedback for output…

Optimization and Control · Mathematics 2014-03-18 Mehrdad Pakmehr , Tansel Yucelen

Traffic congestion has lead to an increasing emphasis on management measures for a more efficient utilization of existing infrastructure. In this context, this paper proposes a novel framework that integrates real-time optimization of…

Systems and Control · Electrical Eng. & Systems 2024-12-20 Samarth Gupta , Ravi Seshadri , Bilge Atasoy , A. Arun Prakash , Francisco Pereira , Gary Tan , Moshe Ben-Akiva

We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…

Statistical Mechanics · Physics 2015-05-13 Daniele De Martino , Luca Dall'Asta , Ginestra Bianconi , Matteo Marsili

To cope with uncertain traffic patterns and traffic models, traffic-responsive signal control strategies in the literature are designed to be robust to these uncertainties. These robust strategies still require sensing infrastructure to…

Systems and Control · Electrical Eng. & Systems 2024-10-08 Leonardo Pedroso , Pedro Batista , Markos Papageorgiou

We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…

Physics and Society · Physics 2019-07-22 Michael Herty , Gabriella Puppo , Sebastiano Roncoroni , Giuseppe Visconti

A macroscopic model is proposed to depict the traffic dynamics involved in urban traffic systems. The link dynamics are described based on the cell-transmission model and bounded by the link capacities, while the flow dynamics are proposed…

Optimization and Control · Mathematics 2020-02-25 Yicheng Zhang

Balancing traffic flow by influencing drivers' route choices to alleviate congestion is becoming increasingly more appealing in urban traffic planning. Here, we introduce a discrete dynamical model comprising users who make their own…

Physics and Society · Physics 2020-09-09 Bo Li , David Saad , Andrey Y. Lokhov

Traffic control is at the core of research in transportation engineering because it is one of the best practices for reducing traffic congestion. It has been shown in recent years that the traffic control problem involving…

Optimization and Control · Mathematics 2021-05-10 Hao Liu , Christian Claudel , Randy Machemehl