Comptes Rendus
First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow
Comptes Rendus. Mécanique, Volume 333 (2005) no. 11, pp. 843-851.

This article deals with a review and critical analysis of first order hydrodynamic models of vehicular traffic flow obtained by the closure of the mass conservation equation. The closure is obtained by phenomenological models suitable to relate the local mean velocity to local density profiles. Various models are described and critically analyzed in the deterministic and stochastic case. The analysis is developed in view of applications of the models to traffic flow simulations for networks of roads. Some research perspectives are derived from the above analysis and proposed in the last part of the paper.

Ce article propose une revue et une analyse critique des modèles hydrodynamiques du trafic routier obtenus par fermeture de l'équation de conservation de la masse. La fermeture est obtenue à partir de modèles phénoménologiques reliant les profils des densités locales à la vitesse moyenne locale. Différents modèles sont décrits et discutés aussi bien dans le cas déterministe que stochastique. L'analyse est développée en vue d'applications aux simulations des modèles de trafic pour les réseaux routiers. Des perspectives de recherche, basées sur notre analyse, sont proposées dans la dernière partie de ce travail.

Published online:
DOI: 10.1016/j.crme.2005.09.004
Keywords: Continuum mechanics, Traffic flow models, Mass conservation, Continuum models, Nonlinear sciences
Mot clés : Milieux continus, Modèles de trafic routier, Équation de conservation de la masse, Modèles continus, Nonlinéarité

Nicola Bellomo 1; Vincenzo Coscia 2

1 Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2 Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy
@article{CRMECA_2005__333_11_843_0,
     author = {Nicola Bellomo and Vincenzo Coscia},
     title = {First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {843--851},
     publisher = {Elsevier},
     volume = {333},
     number = {11},
     year = {2005},
     doi = {10.1016/j.crme.2005.09.004},
     language = {en},
}
TY  - JOUR
AU  - Nicola Bellomo
AU  - Vincenzo Coscia
TI  - First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow
JO  - Comptes Rendus. Mécanique
PY  - 2005
SP  - 843
EP  - 851
VL  - 333
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crme.2005.09.004
LA  - en
ID  - CRMECA_2005__333_11_843_0
ER  - 
%0 Journal Article
%A Nicola Bellomo
%A Vincenzo Coscia
%T First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow
%J Comptes Rendus. Mécanique
%D 2005
%P 843-851
%V 333
%N 11
%I Elsevier
%R 10.1016/j.crme.2005.09.004
%G en
%F CRMECA_2005__333_11_843_0
Nicola Bellomo; Vincenzo Coscia. First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow. Comptes Rendus. Mécanique, Volume 333 (2005) no. 11, pp. 843-851. doi : 10.1016/j.crme.2005.09.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.09.004/

[1] B. Kerner; H. Rehborn Experimental properties of complexity in traffic flow, Phys. Rev. E, Volume 53 (1996), pp. 4275-4278

[2] B. Kerner Experimental features of self-organization in traffic flow, Phys. Rev. Lett., Volume 81 (1998), pp. 3797-3800

[3] B. Kerner Synchronized flow as a new traffic phase and related problems of traffic flow, Math. Comput. Modelling, Volume 35 (2002), pp. 481-508

[4] A. Klar; R.D. Küne; R. Wegener Mathematical models for vehicular traffic, Surveys Math. Ind., Volume 6 (1996), pp. 215-239

[5] A. Klar; R. Wegener Kinetic traffic flow models (N. Bellomo; M. Pulvirenti, eds.), Modeling in Applied Sciences: A Kinetic Theory Approach, Birkhäuser, Boston, 2000

[6] D. Helbing Traffic and related self-driven many-particle systems, Rev. Mod. Phys., Volume 73 (2001), pp. 1067-1141

[7] N. Bellomo; V. Coscia; M. Delitala On the mathematical theory of vehicular traffic flow I—Fluid dynamic and kinetic modeling, Math. Mod. Meth. Appl. Sci., Volume 12 (2002), pp. 1801-1844

[8] S. Darbha; K.R. Rajagopal Limit of a collection of dynamical systems: an application to modelling the flow of traffic, Math. Mod. Meth. Appl. Sci., Volume 12 (2002), pp. 1381-1400

[9] I. Bonzani; L. Mussone From experiments to hydrodynamic traffic flow models. I—Modelling and parameter identification, Math. Comput. Modelling, Volume 37 (2003), pp. 109-119

[10] R. Burger; K.H. Karlsen On a diffusively corrected kinematic-wave traffic flow model with changing road surface conditions, Math. Mod. Meth. Appl. Sci., Volume 13 (2003), pp. 1767-1800

[11] T. Herthy; A. Klar Simplified dynamics and optimization of large scale networks, Math. Mod. Meth. Appl. Sci., Volume 14 (2004), pp. 579-602

[12] V. Astarita Node and link models for network traffic flow simulation, Math. Comput. Modelling, Volume 35 (2002), pp. 643-656

[13] J.P. Lebaque; M. Khoshyaran Modelling vehicular traffic flow on networks using macroscopic models (F. Vilsmeier et al., eds.), Finite Volumes for Complex Applications—Problems and Perspectives, Duisburg Press, Duisburg, 1999

[14] M. Lighthill; J.B. Whitham On kinematic waves. I: Flow movement in long rivers. II: A theory of traffic flow on long crowded roads, Proc. Royal Soc. Edinburgh A, Volume 229 (1955), pp. 281-345

[15] H.J. Payne, Models of Freeway Traffic and Control, Simulation Council, New York, 1971

[16] E. De Angelis Nonlinear hydrodynamic models of traffic flow modelling and mathematical problems, Math. Comput. Modelling, Volume 29 (1999), pp. 83-95

[17] C. Daganzo Requiem for second order fluid approximations of traffic flow, Transp. Res. B, Volume 29 (1995), pp. 277-286

[18] A. Aw; M. Rascle Resurrection of “second order models” of traffic flow, SIAM J. Appl. Math., Volume 60 (2000), pp. 916-938

[19] I. Bonzani Hydrodynamic models of traffic flow—drivers behavior and nonlinear diffusion, Math. Comput. Modelling, Volume 31 (2000), pp. 1-8

[20] V. Coscia On the closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flow, C. R. Mécanique, Volume 332 (2004), pp. 585-590

[21] N. Bellomo; A. Marasco; A. Romano From the modelling of driver's behaviour to hydrodynamic models and problems of traffic flow, Nonlinear Anal., Volume 3 (2002), pp. 339-363

[22] M.L. Bertotti; N. Bellomo Boundary value steady solutions of a class of hydrodynamic models for vehicular traffic flow models, Math. Comput. Modelling, Volume 38 (2003), pp. 367-383

[23] A.D. May Traffic Flow Fundamentals, Prentice Hall, Englewood Cliffs, 1990

[24] M. Delitala Nonlinear models of traffic flow. New frameworks of mathematical kinetic theory, C. R. Mécanique, Volume 331 (2003), pp. 817-822

[25] S. Darbha; K.R. Rajagopal Aggregation of a class of interconnected linear dynamical systems, Systems Control Lett., Volume 43 (2001), pp. 387-401

[26] S. Darbha; K.R. Rajagopal Aggregation of a class of large scale interconnected, nonlinear dynamical systems, Math. Problems Engrg., Volume 7 (2001), pp. 379-392

Cited by Sources:

Comments - Policy