# American Institute of Mathematical Sciences

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

## Linear model of traffic flow in an isolated network

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 A related model which used outdated information is shown to collapse in finite time.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