On the mathematical theory of vehicular traffic flow II: Discrete velocity kinetic models
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The discretization overcomes, at least in part, some technical difficulties related to the selection of the correct representation scale, while the adaptative grid allows an improved description of various phenomena related to vehicular traffic flow.Abstract:
This paper deals with the modelling of vehicular traffic flow by methods of the discrete mathematical kinetic theory. The discretization is developed in the velocity space by a grid adapted to the local density. The discretization overcomes, at least in part, some technical difficulties related to the selection of the correct representation scale, while the adaptative grid allows an improved description of various phenomena related to vehicular traffic flow. Specific models are proposed and a qualitative and computational analysis is developed to show the properties of the model and their ability to describe real flow conditions. A critical analysis, proposed in the last part of the paper, outlines suitable research perspectives.read more
Citations
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References
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Traffic and related self-driven many-particle systems
Dirk Helbing,Dirk Helbing +1 more
TL;DR: This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic, including microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models.
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Requiem for second-order fluid approximations of traffic flow
TL;DR: In this paper, it is shown that any continuum model of traffic flow that smooths out all discontinuities in density will predict negative flows and negative speeds (i.e., "wrong way travel") under certain conditions.
Book
Kinetic theory of vehicular traffic
TL;DR: A theory of multi-LANE traffic flow and the space-time evolution of thevelocity distribution of cars are examined to help understand the role of driver behaviour and strategy in this network.
Journal ArticleDOI
On Boltzmann-like treatments for traffic flow: A critical review of the basic model and an alternative proposal for dilute traffic analysis
TL;DR: The basic features of the Boltzmann-like model for traffic flow, due to Prigogine and coworkers, are reviewed and an alternative model is proposed for dilute traffic conditions.
Journal Article
The Physics of Traffic: Empirical Freeway Pattern Features, Engineering Applications, and Theory
TL;DR: This book introduces a new traffic flow theory called "three-phase traffic theory," which can explain empirical spatiotemporal traffic patterns and results of an application of the pattern features to engineering applications without complex mathematical models.