American Institute of Mathematical Sciences

Advanced
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

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 A related model which used outdated information is shown to collapse in finite time.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).   Google Scholar

[2]

J. K. Hale, L. T. Magalhaes and W. M. Oliva, Dynamics in Infinite Dimensions,, Springer-Verlag, (2002).   Google Scholar

[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.   Google Scholar

[4]

A. Jiménez-Casas and A. Rodríguez-Bernal, General model of traffic flow in an isolated network,, in preparation., ().   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

show all references

References:
[1]

J. K. Hale, Theory of Functional Differential Equations,, Springer-Verlag, (1977).   Google Scholar

[2]

J. K. Hale, L. T. Magalhaes and W. M. Oliva, Dynamics in Infinite Dimensions,, Springer-Verlag, (2002).   Google Scholar

[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.   Google Scholar

[4]

A. Jiménez-Casas and A. Rodríguez-Bernal, General model of traffic flow in an isolated network,, in preparation., ().   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

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