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Related papers: The Aw-Rascle-Zhang model with constraints

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We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…

Classical Physics · Physics 2007-05-23 S. Tim Hatamian

This paper deals with the modeling and numerical simulations of multilane vehicular traffic according to the discrete kinetic theory approach. The nonlinear additive interactions and external actions such as tollgates as well traffic signs…

Analysis of PDEs · Mathematics 2023-11-28 Mohamed Zagour

This paper investigates the problem of computing a two-dimensional optimal curvature straight line (CS) shortest path for an unmanned aerial vehicle (UAV) to intercept a moving target, with both the UAV (pursuer) and target travelling at…

Optimization and Control · Mathematics 2025-07-03 Masuda Akter , Mohammed Mustafa Rizvi

We study a generalized Follow-the-Leader model where the driver considers the position of an arbitrary but finite number of vehicles ahead, as well as the position of the vehicle directly behind the driver. It is proved that this model…

Analysis of PDEs · Mathematics 2024-05-08 Helge Holden , Nils Henrik Risebro

Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image…

Numerical Analysis · Mathematics 2018-01-15 Roland Herzog , John W. Pearson , Martin Stoll

While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with…

Statistical Mechanics · Physics 2009-11-10 Dirk Helbing

We present a novel framework for modeling traffic congestion events over road networks. Using multi-modal data by combining count data from traffic sensors with police reports that report traffic incidents, we aim to capture two types of…

Machine Learning · Computer Science 2021-06-02 Shixiang Zhu , Ruyi Ding , Minghe Zhang , Pascal Van Hentenryck , Yao Xie

Based on a Boltzmann-like traffic equation for aggressive drivers we construct in this paper a second-order continuum traffic model which is similar to the Navier-Stokes equations for viscous fluids by applying two well-known methods of…

Mathematical Physics · Physics 2010-12-01 W. Marques , A. R. Mendez

We prove the non-linear stability of a class of travelling-wave solutions to the extended Aw-Rascle system with a singular offset function, which is formally equivalent to the compressible pressureless Navier-Stokes system with a singular…

Analysis of PDEs · Mathematics 2024-04-29 Émile Deléage , Muhammed Ali Mehmood

Traffic waves, the spatiotemporal propagation of congestion, are a key feature of traffic flow. As Adaptive Cruise Control (ACC) systems gain widespread adoption and show promise for improving both efficiency and safety, understanding how…

Analysis of PDEs · Mathematics 2026-02-03 Zihao Li , Quyuan Lin , Fan Pu , Soyoung Ahn , Yunlong Zhang , Jiwan Jiang , Yang Zhou

The first part of this paper contains a brief introduction to conservation law models of traffic flow on a network of roads. Globally optimal solutions and Nash equilibrium solutions are reviewed, with several groups of drivers sharing…

Analysis of PDEs · Mathematics 2019-01-18 Alberto Bressan , Yucong Huang

The constrained transport (CT) method reflects the state of the art numerical technique for preserving the divergence-free condition of magnetic field to machine accuracy in multi-dimensional MHD simulations performed with Godunov-type, or…

Computational Physics · Physics 2020-12-02 Andrea Mignone , Luca Del Zanna

The implementation of road user models that realistically reproduce a credible behavior in a multi-agentsimulation is still an open problem. A data-driven approach consists on to deduce behaviors that may exist in real situation to obtain…

Artificial Intelligence · Computer Science 2024-07-04 Nelson de Moura , Augustin Gervreau-Mercier , Fernando Garrido , Fawzi Nashashibi

Traffic simulators act as an essential component in the operating and planning of transportation systems. Conventional traffic simulators usually employ a calibrated physical car-following model to describe vehicles' behaviors and their…

Artificial Intelligence · Computer Science 2022-07-12 Guanjie Zheng , Hanyang Liu , Kai Xu , Zhenhui Li

A recently introduced two-phase flow model by Chun Shen is studied in this work. The model is derived to describe the dynamics of immersed water bubbles in liquid water as carrier. Several assumptions are made to obtain a reduced form of…

Fluid Dynamics · Physics 2025-12-03 Abdul Rab

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

We prove existence and uniqueness of solutions to a transport equation modelling vehicular traffic in which the velocity field depends non-locally on the downstream traffic density via a discontinuous anisotropic kernel. The result is…

Analysis of PDEs · Mathematics 2015-10-16 Paola Goatin , Francesco Rossi

We present a new approach for search of coexisting classes of localised modes admitted by the repulsive (defocusing) scalar or vector nonlinear Schr\"odinger-type equations. The approach is based on the observation that generic solutions of…

Pattern Formation and Solitons · Physics 2019-04-10 G. L. Alfimov , I. V. Barashenkov , A. P. Fedotov , V. V. Smirnov , D. A. Zezyulin

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

Monitoring and control of traffic networks represent alternative, inexpensive strategies to minimize traffic congestion. As the number of traffic sensors is naturally constrained by budgetary requirements, real-time estimation of traffic…

Systems and Control · Computer Science 2019-11-12 Sebastian A. Nugroho , Ahmad F. Taha , Christian Claudel