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 A related model which used outdated information is shown to collapse in finite time.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, New York, (1977).  Google Scholar

[2]

J. K. Hale, L. T. Magalhaes and W. M. Oliva, Dynamics in Infinite Dimensions, Springer-Verlag, New York, (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, SEMA/SIMAI Springer Series, 4 (2014), 193-200, ISBN 978-3-319-06952-4.  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), 1962-1968. 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(4) (2007), 569-594.  Google Scholar

show all references

References:
[1]

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

[2]

J. K. Hale, L. T. Magalhaes and W. M. Oliva, Dynamics in Infinite Dimensions, Springer-Verlag, New York, (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, SEMA/SIMAI Springer Series, 4 (2014), 193-200, ISBN 978-3-319-06952-4.  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), 1962-1968. 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(4) (2007), 569-594.  Google Scholar

[1]

Mary Luz Mouronte, Rosa María Benito. Structural analysis and traffic flow in the transport networks of Madrid. Networks & Heterogeneous Media, 2015, 10 (1) : 127-148. doi: 10.3934/nhm.2015.10.127
[2]

Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Numerical approximations of a traffic flow model on networks. Networks & Heterogeneous Media, 2006, 1 (1) : 57-84. doi: 10.3934/nhm.2006.1.57
[3]

Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Fast algorithms for the approximation of a traffic flow model on networks. Discrete & Continuous Dynamical Systems - B, 2006, 6 (3) : 427-448. doi: 10.3934/dcdsb.2006.6.427
[4]

Paola Goatin. Traffic flow models with phase transitions on road networks. Networks & Heterogeneous Media, 2009, 4 (2) : 287-301. doi: 10.3934/nhm.2009.4.287
[5]

Alberto Bressan, Ke Han. Existence of optima and equilibria for traffic flow on networks. Networks & Heterogeneous Media, 2013, 8 (3) : 627-648. doi: 10.3934/nhm.2013.8.627
[6]

Emiliano Cristiani, Fabio S. Priuli. A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks. Networks & Heterogeneous Media, 2015, 10 (4) : 857-876. doi: 10.3934/nhm.2015.10.857
[7]

Gabriella Bretti, Maya Briani, Emiliano Cristiani. An easy-to-use algorithm for simulating traffic flow on networks: Numerical experiments. Discrete & Continuous Dynamical Systems - S, 2014, 7 (3) : 379-394. doi: 10.3934/dcdss.2014.7.379
[8]

Maya Briani, Emiliano Cristiani. An easy-to-use algorithm for simulating traffic flow on networks: Theoretical study. Networks & Heterogeneous Media, 2014, 9 (3) : 519-552. doi: 10.3934/nhm.2014.9.519
[9]

Lino J. Alvarez-Vázquez, Néstor García-Chan, Aurea Martínez, Miguel E. Vázquez-Méndez. Optimal control of urban air pollution related to traffic flow in road networks. Mathematical Control & Related Fields, 2018, 8 (1) : 177-193. doi: 10.3934/mcrf.2018008
[10]

Alberto Bressan, Khai T. Nguyen. Optima and equilibria for traffic flow on networks with backward propagating queues. Networks & Heterogeneous Media, 2015, 10 (4) : 717-748. doi: 10.3934/nhm.2015.10.717
[11]

Emiliano Cristiani, Smita Sahu. On the micro-to-macro limit for first-order traffic flow models on networks. Networks & Heterogeneous Media, 2016, 11 (3) : 395-413. doi: 10.3934/nhm.2016002
[12]

Yacine Chitour, Benedetto Piccoli. Traffic circles and timing of traffic lights for cars flow. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 599-630. doi: 10.3934/dcdsb.2005.5.599
[13]

P. Adda, J. L. Dimi, A. Iggidir, J. C. Kamgang, G. Sallet, J. J. Tewa. General models of host-parasite systems. Global analysis. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 1-17. doi: 10.3934/dcdsb.2007.8.1
[14]

G. C. Yang, K. Q. Lan. Systems of singular integral equations and applications to existence of reversed flow solutions of Falkner-Skan equations. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2465-2495. doi: 10.3934/cpaa.2013.12.2465
[15]

Radu C. Cascaval, Ciro D'Apice, Maria Pia D'Arienzo, Rosanna Manzo. Flow optimization in vascular networks. Mathematical Biosciences & Engineering, 2017, 14 (3) : 607-624. doi: 10.3934/mbe.2017035
[16]

Mapundi K. Banda, Michael Herty, Axel Klar. Gas flow in pipeline networks. Networks & Heterogeneous Media, 2006, 1 (1) : 41-56. doi: 10.3934/nhm.2006.1.41
[17]

Alessia Marigo. Optimal traffic distribution and priority coefficients for telecommunication networks. Networks & Heterogeneous Media, 2006, 1 (2) : 315-336. doi: 10.3934/nhm.2006.1.315
[18]

Ye Sun, Daniel B. Work. Error bounds for Kalman filters on traffic networks. Networks & Heterogeneous Media, 2018, 13 (2) : 261-295. doi: 10.3934/nhm.2018012
[19]

Yong Ren, Huijin Yang, Wensheng Yin. Weighted exponential stability of stochastic coupled systems on networks with delay driven by $ G $-Brownian motion. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3379-3393. doi: 10.3934/dcdsb.2018325
[20]

Matteo Petrera, Yuri B. Suris. Geometry of the Kahan discretizations of planar quadratic Hamiltonian systems. Ⅱ. Systems with a linear Poisson tensor. Journal of Computational Dynamics, 2019, 6 (2) : 401-408. doi: 10.3934/jcd.2019020

 Impact Factor: 

Tools

Metrics

  • PDF downloads (37)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences