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Related papers: A kinetic traffic network model and its macroscopi…

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This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…

Probability · Mathematics 2021-02-11 Michel Mandjes , Jaap Storm

In this paper, we study a general class of inhomogeneous kinetic models that unifies fundamental models in both the statistical physics of particles and of waves, namely the kinetic Boltzmann equations and the kinetic wave equations, in…

Analysis of PDEs · Mathematics 2026-04-10 Manh Hong Duong , Zihui He

Based on experimental traffic data obtained from German and US highways, we propose a novel two-dimensional first-order macroscopic traffic flow model. The goal is to reproduce a detailed description of traffic dynamics for the real road…

Physics and Society · Physics 2017-11-10 Michael Herty , Adrian Fazekas , Giuseppe Visconti

In this paper, we present a class of systems of non-local conservation laws in one space-dimension incorporating time delay, which can be used to investigate the interaction between autonomous and human-driven vehicles, each characterized…

Analysis of PDEs · Mathematics 2025-01-17 Ilaria Ciaramaglia , Paola Goatin , Gabriella Puppo

The emergence of congestion is a critical phenomenon in transport systems. Transport is organized along pathways abstracted by links, which connect different nodes as regions to form the network. The modeling of traffic has so far mainly…

Physics and Society · Physics 2023-03-23 Zhidong He

In this paper we propose a new modeling technique for vehicular traffic flow, designed for capturing at a macroscopic level some effects, due to the microscopic granularity of the flow of cars, which would be lost with a purely continuous…

Mathematical Physics · Physics 2014-03-25 Emiliano Cristiani , Benedetto Piccoli , Andrea Tosin

We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…

Statistical Mechanics · Physics 2007-05-23 Dafang Zheng , Guler Ergun

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 develop a discrete Boltzmann-type model that uses dynamics in phase space to describe the behavior of traffic flows. Firstly, we model the traffic flow at mesoscopic scale using dynamics in phase space, which is considered as an…

Cellular Automata and Lattice Gases · Physics 2023-11-27 Zhizhen Zhang , Changhong Lu

Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics such as links, paths, cycles, and components are obtained analytically using the rate…

Statistical Mechanics · Physics 2007-05-23 E. Ben-Naim , P. L. Krapivsky

Starting from the concept of binary interactions between pairs of particles, a kinetic framework for the description of the action potential dynamics on a neural network is proposed. It consists of two coupled levels: the description of a…

Biological Physics · Physics 2023-03-21 Martina Conte , Maria Groppi , Andrea Tosin

The communication networks in real world often couple with each other to save costs, which results in any network does not have a stand-alone function and efficiency. To investigate this, in this paper we propose a transportation model on…

Physics and Society · Physics 2016-12-19 Ming Li , Mao-Bin Hu , Bing-Hong Wang

Climate change compels a reduction of greenhouse gas emissions, yet vehicular traffic still contributes significantly to the emission of air pollutants. Hence, in this paper we focus on the optimization of traffic flow while simultaneously…

Optimization and Control · Mathematics 2024-06-10 Simone Göttlich , Michael Herty , Alena Ulke

We consider transport networks with nodes scattered at random in a large domain. At certain local rates, the nodes generate traffic flowing according to some navigation scheme in a given direction. In the thermodynamic limit of a growing…

Probability · Mathematics 2016-02-03 Christian Hirsch , Benedikt Jahnel , Paul Keeler , Robert I. A. Patterson

We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle…

Condensed Matter · Physics 2009-10-22 Satoshi Yukawa , Macoto Kikuchi

This work studies a macroscopic traffic flow model driven by a system of nonlinear hyperbolic partial differential equations. Using Lie symmetry analysis, we determine the infinitesimal generators and construct an optimal system of…

Analysis of PDEs · Mathematics 2025-08-26 Urvashi Joshi , Aniruddha Kumar Sharma , Rajan Arora

We consider a conservation law model of traffic flow, where the velocity of each car depends on a weighted average of the traffic density $\rho$ ahead. The averaging kernel is of exponential type: $w_\varepsilon(s)=\varepsilon ^{-1}…

Analysis of PDEs · Mathematics 2020-05-20 Alberto Bressan , Wen Shen

We introduce microscopic and macroscopic stochastic traffic models including traffic accidents. The microscopic model is based on a Follow-the-Leader approach whereas the macroscopic model is described by a scalar conservation law with…

Probability · Mathematics 2021-11-19 Simone Göttlich , Thomas Schillinger

The present paper proposes a stochastic model of the traffic flow. This model has a discrete set of states and the continuous time. The model is a generalization of the discrete stochastis model that has been considered in a previous paper…

Other Condensed Matter · Physics 2007-05-23 A. P. Buslaev , A. G. Tatashev , M. V. Yashina

Kinetics of dilute heterogeneous traffic on a two lane road is formulated in the framework of the Ben-Naim Krapivsky model and stationary state properties are analytically derived in the asymptotic limit. The heterogeneity is introduced as…

Physics and Society · Physics 2022-08-02 A. Sai Venkata Ramana , Saif Eddin Jabari