On the mathematical theory of vehicular traffic flow II: Discrete velocity kinetic models

被引：51

作者：

Coscia, V. ^{[1
]}

Delitala, M.

Frasca, P.

机构：

[1] Univ Ferrara, Dept Math, I-44100 Ferrara, Italy

[2] Politecn Turin, Dept Math, Turin, Italy

来源：

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2007年 / 42卷 / 03期

关键词：

traffic flow; kinetic theory; non-linear sciences; multiscale modelling;

D O I：

10.1016/j.ijnonlinmec.2006.02.008

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

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. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：411 / 421

页数：11

共 31 条

[1] Generalized kinetic (Boltzmann) models: Mathematical structures and applications [J].

Arlotti, L ;

Bellomo, N ;

De Angelis, E .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (04) :567-591

[2]

ARLOTTI L, 2003, LECT NOTES MATH PROB

[3]

Astarita V, 2002, MATH COMPUT MODEL, V35, P643, DOI 10.1016/S0895-7177(02)80026-7

[4] First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow [J].

Bellomo, N ;

Coscia, V .

COMPTES RENDUS MECANIQUE, 2005, 333 (11) :843-851

[5] On the mathematical theory of vehicular traffic flow - I. Fluid dynamic and kinetic modelling [J].

Bellomo, N ;

Delitala, M ;

Coscia, V .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (12) :1801-1843

[6]

Bellomo N., 2003, LECT NOTES DISCRETIZ

[7] Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems [J].

Bellomo, Nicola ;

Forni, Guido .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2006, 16 (07) :1001-1029

[8] Mathematical methods and tools of kinetic theory towards modelling complex biological systems [J].

Bellouquid, A ;

Delitala, M .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2005, 15 (11) :1639-1666

[9] From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences [J].

Bertotti, ML ;

Delitala, M .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2004, 14 (07) :1061-1084

[10] Stochastic modelling of traffic flow [J].

Bonzani, I ;

Mussone, L .

MATHEMATICAL AND COMPUTER MODELLING, 2002, 36 (1-2) :109-119

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