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Related papers: Second-order traffic flow models on networks

200 papers

This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it…

Physics and Society · Physics 2015-05-13 Dirk Helbing

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

This paper presents scalable traffic stability analysis for both pure autonomous vehicle (AV) traffic and mixed traffic based on continuum traffic flow models. Human vehicles are modeled by a non-equilibrium traffic flow model, i.e.,…

Optimization and Control · Mathematics 2024-09-23 Kuang Huang , Xuan Di , Qiang Du , Xi Chen

A modular fluid-flow model for network congestion analysis and control is proposed. The model is derived from an information conservation law stating that the information is either in transit, lost or received. Mathematical models of…

Networking and Internet Architecture · Computer Science 2012-08-07 Corentin Briat , Emre Altug Yavuz , Gunnar Karlsson

In this Letter we suggest a simple and physically transparent analytical model of the pressure driven turbulent wall-bounded flows at high but finite Reynolds numbers Re. The model gives accurate qualitative description of the profiles of…

Chaotic Dynamics · Physics 2009-02-18 Victor S. L'vov , Itamar Procaccia , Oleksii Rudenko

Kinetic models for vehicular traffic are reviewed and considered from the point of view of deriving macroscopic equations. A derivation of the associated macroscopic traffic flow equations leads to different types of equations: in certain…

Numerical Analysis · Mathematics 2015-03-13 Raul Borsche , Axel Klar , Mark Kimathi

In traffic signal control, flow-based (optimizing the overall flow) and pressure-based methods (equalizing and alleviating congestion) are commonly used but often considered separately. This study introduces a unified framework using…

Systems and Control · Electrical Eng. & Systems 2024-01-18 Chaolun Ma , Bruce Wang , Zihao Li , Ahmadreza Mahmoudzadeh , Yunlong Zhang

For a class of data-fitted macroscopic traffic models, the influence of the choice of the stagnation density on the model accuracy is investigated. This work builds on an established framework of data-fitted first-order…

Physics and Society · Physics 2013-08-05 Shimao Fan , Benjamin Seibold

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

Nowadays, traffic management has become a challenge for urban areas, which are covering larger geographic spaces and facing the generation of different kinds of traffic data. This article presents a robust traffic estimation framework for…

Optimization and Control · Mathematics 2016-06-13 Edward S. Canepa , Christian G. Claudel

A novel constructive mathematical model based on the multifractal formalism in order to accurately characterizing the localized fluctuations present in the course of traffic flows today high-speed computer networks is presented. The…

Networking and Internet Architecture · Computer Science 2021-06-29 G. Millán , G. Lefranc , R. Osorio-Comparán

This paper analyzes the vanishing pressure limit of solutions to the Aw-Rascle model and the perturbed Aw-Rascle model for modified Chaplygin gas. Firstly, the Riemann problem of the Aw-Rascle model is solved constructively. A special delta…

Analysis of PDEs · Mathematics 2014-10-07 Jinhuan Wang , Jinjing Liu , Hanchun Yang

A macroscopic model-based approach for estimation of the traffic state, specifically of the (total) density and flow of vehicles, is developed for the case of "mixed" traffic, i.e., traffic comprising both ordinary and connected vehicles.…

Optimization and Control · Mathematics 2015-04-28 Nikolaos Bekiaris-Liberis , Claudio Roncoli , Markos Papageorgiou

Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…

Statistics Theory · Mathematics 2025-12-11 Gonzalo Mena , Arun Kumar Kuchibhotla , Larry Wasserman

In the setting of a recently developed cellular stochastic traffic flow model, it has shown that the joint per-cell vehicle densities, as a function of time, can be accurately approximated by a Gaussian process, which has the attractive…

Optimization and Control · Mathematics 2020-07-16 Michel Mandjes , Jaap Storm

A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behavior for the solid…

Fluid Dynamics · Physics 2019-04-10 Tobias Ahnert , Andreas Münch , Barbara Wagner

Modeling transition-continuum hypersonic flows poses significant challenges due to thermodynamic nonequilibrium and the associated breakdown of the continuum assumption. Standard continuum models such as the Navier-Stokes equations are…

Fluid Dynamics · Physics 2025-06-18 Mikolaj Kryger , Jonathan F. MacArt

This paper develops boundary feedback controls to stabilize traffic congestion toward a predefined shock equilibrium in the Aw-Rascle-Zhang (ARZ) traffic flow model. We transform the corresponding moving-boundary $2\times2$ hyperbolic…

Optimization and Control · Mathematics 2026-04-03 Mina Cao , Mamadou Diagne , Peipei Shang , Lei Yu

This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be "transported" to a…

Optimization and Control · Mathematics 2022-04-28 Ferran Arqué , César A. Uribe , Carlos Ocampo-Martinez

We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…

Numerical Analysis · Mathematics 2016-10-06 Herbert Egger