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Related papers: Traffic Flow Models and Their Numerical Solutions

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We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average…

Optimization and Control · Mathematics 2019-11-11 Simone Cacace , Fabio Camilli , Raul De Maio , Andrea Tosin

In this paper, we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads. On individual roads, we consider the standard Lighthill-Whitham-Richards model which is discretized using the…

Numerical Analysis · Mathematics 2020-11-24 Lukáš Vacek , Václav Kučera

The objective of this paper is to initiate a qualitative analysis of dynamic flow in traffic networks by using the competitive equilibrium model of multiple market systems. A network is modeled as a dynamic graph where routes (edges) are…

Systems and Control · Computer Science 2017-11-30 Dragoslav D. Šiljak

Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal…

Physics and Society · Physics 2013-10-21 Mark J Panaggio , Bertrand J Ottino-Löffler , Peiguang Hu , Daniel M Abrams

We propose a macroscopic traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as…

Systems and Control · Computer Science 2015-05-25 Samuel Coogan , Murat Arcak

We investigate a model for traffic flow based on the Lighthill-Whitham-Richards model that consists of a hyperbolic conservation law with a discontinuous, piecewise-linear flux. A mollifier is used to smooth out the discontinuity in the…

Numerical Analysis · Mathematics 2013-05-17 Jeffrey K. Wiens , John M. Stockie , JF Williams

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

We present a multilane traffic model based on balance laws, where the nonlocal source term is used to describe the lane changing rate. The modelling framework includes the consideration of local and nonlocal flux functions. Based on a…

Numerical Analysis · Mathematics 2022-09-08 Jan Friedrich , Simone Göttlich , Elena Rossi

The interest in developing smart cities has increased dramatically in recent years. In this context an intelligent transportation system depicts a major topic. The forecast of traffic flow is indispensable for an efficient intelligent…

Machine Learning · Computer Science 2020-06-09 Ralf Rüther , Andreas Klos , Marius Rosenbaum , Wolfram Schiffmann

This paper presents a mixed traffic control policy designed to optimize traffic efficiency across diverse road topologies, addressing issues of congestion prevalent in urban environments. A model-free reinforcement learning (RL) approach is…

Robotics · Computer Science 2025-01-29 Chuyang Xiao , Dawei Wang , Xinzheng Tang , Jia Pan , Yuexin Ma

The Logit lane assignment model has been introduced recently in order to describe multi-lane traffic flow from a macroscopic point of view. The model is based on the idea that each available lane has a specific utility for each driver, who…

Nonlinear hyperbolic partial differential equations govern continuum traffic flow models. Higher-order traffic flow models consisting of continuum equations and velocity dynamics were introduced to address the limitations of the Lighthill,…

Analysis of PDEs · Mathematics 2024-07-10 Nandan Maiti , Bhargava Rama Chilukuri

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

To gain essential understandings of traffic flow, four theorems are derived to establish the kinematics of the basic unit of traffic flow, namely two consecutive vehicles. The first is to determine the two critical distances of the vehicle…

Physics and Society · Physics 2022-12-21 Xin Shui

To study gap acceptance behaviour one needs the distribution (or probability density function) of gaps in the opposing stream. Further, in these times of widespread availability of large computing powers, traffic simulation has emerged as a…

Applications · Statistics 2025-12-10 Ankita Sharma , Partha Chakroborty , Pranamesh Chakraborty

Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on…

Probability · Mathematics 2017-08-22 Harsha Honnappa , Rahul Jain

We consider solutions of the Aw-Rascle model for traffic flow fulfilling a constraint on the flux at $x=0$. Two different kinds of solutions are proposed: at $x=0$ the first one conserves both the number of vehicles and the generalized…

Analysis of PDEs · Mathematics 2010-07-01 Mauro Garavello , Paola Goatin

The traffic assignment problem is one of the significant components of traffic flow analysis for which various solution approaches have been proposed. However, deploying these approaches for large-scale networks poses significant…

Machine Learning · Computer Science 2024-10-18 Tong Liu , Hadi Meidani

Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…

Discrete Mathematics · Computer Science 2017-05-24 Fabian Mies , Britta Peis , Andreas Wierz

Many real life queueing networks have finite buffers with overflows. To understand the behavior of such networks, we consider traffic equations that generalize the traffic equations of classic open queueing networks where some nodes are…

Optimization and Control · Mathematics 2020-12-11 S. Fleuren , H. M. Jansen , E. Lefeber , Y. Nazarathy