Linear model of traffic flow in an isolated network

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2015, 2015(special): 670-677. doi: 10.3934/proc.2015.0670

Linear model of traffic flow in an isolated network

Ángela Jiménez-Casas ^1, and Aníbal Rodríguez-Bernal ^2,

1.	Grupo de Dinámica No Lineal. Universidad Pontificia Comillas de Madrid, C/Alberto Agulilera 23, 28015 Madrid
2.	Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain

Received September 2014 Revised April 2015 Published November 2015

Abstract
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We obtain a mathematical linear model which describes automatic operation of the traffic of material objects in a network. Existence and global solutions is obtained for such model. A related model which used outdated information is shown to collapse in finite time.

Keywords: traffic flow, Networks, delay integral systems..

Mathematics Subject Classification: Primary: 34K06, 34A33; Secondary: 34A12, 34A3.

Citation: Ángela Jiménez-Casas, Aníbal Rodríguez-Bernal. Linear model of traffic flow in an isolated network. Conference Publications, 2015, 2015 (special) : 670-677. doi: 10.3934/proc.2015.0670

References:

[1]	J. K. Hale, Theory of Functional Differential Equations,, Springer-Verlag, (1977).
[2]	J. K. Hale, L. T. Magalhaes and W. M. Oliva, Dynamics in Infinite Dimensions,, Springer-Verlag, (2002).
[3]	A. Jiménez-Casas and A. Rodríguez-Bernal, A Model of Traffic Flow in a Network,, Advances in Differential Equations and Applications, 4 (2014), 193.
[4]	A. Jiménez-Casas and A. Rodríguez-Bernal, General model of traffic flow in an isolated network,, in preparation., ().
[5]	B. Sridhar and P. K. Menon, Comparison of Linear Dynamic Models for Air Traffic Flow Management,, Proceedings of the 16th IFAC World Congress, (2005), 1962.
[6]	D. Sun, I. S. Strub and A. M. Bayen, Comparison of the Performance of Four Eulerian Network Flow Models for Strategic Air Traffic Network Flow Models for Strategic Air Traffic Management,, Networks and Heterogeneous Media, 2 (2007), 569.

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References:

[1]	J. K. Hale, Theory of Functional Differential Equations,, Springer-Verlag, (1977).
[2]	J. K. Hale, L. T. Magalhaes and W. M. Oliva, Dynamics in Infinite Dimensions,, Springer-Verlag, (2002).
[3]	A. Jiménez-Casas and A. Rodríguez-Bernal, A Model of Traffic Flow in a Network,, Advances in Differential Equations and Applications, 4 (2014), 193.
[4]	A. Jiménez-Casas and A. Rodríguez-Bernal, General model of traffic flow in an isolated network,, in preparation., ().
[5]	B. Sridhar and P. K. Menon, Comparison of Linear Dynamic Models for Air Traffic Flow Management,, Proceedings of the 16th IFAC World Congress, (2005), 1962.
[6]	D. Sun, I. S. Strub and A. M. Bayen, Comparison of the Performance of Four Eulerian Network Flow Models for Strategic Air Traffic Network Flow Models for Strategic Air Traffic Management,, Networks and Heterogeneous Media, 2 (2007), 569.

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