American Institute of Mathematical Sciences

Advanced
June  2006, 1(2): 315-336. doi: 10.3934/nhm.2006.1.315

Optimal traffic distribution and priority coefficients for telecommunication networks

Alessia Marigo 1,

1. 

Dipartimento di Matematica "G. Castelnuovo", Università di Roma "La Sapienza", Viale del Policlinico 137, 00161 Rome, Italy

Received  November 2005 Revised  February 2006 Published  March 2006

The aim of this paper is to optimize tra±c distribution coefficients in order to maximize the trasmission speed of packets over a network. We consider a macroscopic fluidodynamic model dealing with packets flow proposed in [10], where the dynamics at nodes (routers) is decided by a routing algorithm depending on traffic distribution (and priority) coefficients. We solve the general problem for a node with m incoming and n outgoing lines and explicit the optimal parameters for the simple case of two incoming and two outgoing lines.
Keywords: conservation laws, Traffic flow on networks, optimization..
Mathematics Subject Classification: 90B18, 35L6.
Citation: Alessia Marigo. Optimal traffic distribution and priority coefficients for telecommunication networks. Networks and Heterogeneous Media, 2006, 1 (2) : 315-336. doi: 10.3934/nhm.2006.1.315
[1]

Wen Shen. Traveling waves for conservation laws with nonlocal flux for traffic flow on rough roads. Networks and Heterogeneous Media, 2019, 14 (4) : 709-732. doi: 10.3934/nhm.2019028
[2]

Martin Gugat, Alexander Keimer, Günter Leugering, Zhiqiang Wang. Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks. Networks and Heterogeneous Media, 2015, 10 (4) : 749-785. doi: 10.3934/nhm.2015.10.749
[3]

Mauro Garavello. A review of conservation laws on networks. Networks and Heterogeneous Media, 2010, 5 (3) : 565-581. doi: 10.3934/nhm.2010.5.565
[4]

Georges Bastin, B. Haut, Jean-Michel Coron, Brigitte d'Andréa-Novel. Lyapunov stability analysis of networks of scalar conservation laws. Networks and Heterogeneous Media, 2007, 2 (4) : 751-759. doi: 10.3934/nhm.2007.2.751
[5]

Alberto Bressan, Khai T. Nguyen. Conservation law models for traffic flow on a network of roads. Networks and Heterogeneous Media, 2015, 10 (2) : 255-293. doi: 10.3934/nhm.2015.10.255
[6]

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
[7]

Mary Luz Mouronte, Rosa María Benito. Structural analysis and traffic flow in the transport networks of Madrid. Networks and Heterogeneous Media, 2015, 10 (1) : 127-148. doi: 10.3934/nhm.2015.10.127
[8]

Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Numerical approximations of a traffic flow model on networks. Networks and Heterogeneous Media, 2006, 1 (1) : 57-84. doi: 10.3934/nhm.2006.1.57
[9]

Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Fast algorithms for the approximation of a traffic flow model on networks. Discrete and Continuous Dynamical Systems - B, 2006, 6 (3) : 427-448. doi: 10.3934/dcdsb.2006.6.427
[10]

Paola Goatin. Traffic flow models with phase transitions on road networks. Networks and Heterogeneous Media, 2009, 4 (2) : 287-301. doi: 10.3934/nhm.2009.4.287
[11]

Alberto Bressan, Ke Han. Existence of optima and equilibria for traffic flow on networks. Networks and Heterogeneous Media, 2013, 8 (3) : 627-648. doi: 10.3934/nhm.2013.8.627
[12]

Markus Musch, Ulrik Skre Fjordholm, Nils Henrik Risebro. Well-posedness theory for nonlinear scalar conservation laws on networks. Networks and Heterogeneous Media, 2022, 17 (1) : 101-128. doi: 10.3934/nhm.2021025
[13]

Stefano Bianchini. On the shift differentiability of the flow generated by a hyperbolic system of conservation laws. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 329-350. doi: 10.3934/dcds.2000.6.329
[14]

Christophe Chalons, Paola Goatin, Nicolas Seguin. General constrained conservation laws. Application to pedestrian flow modeling. Networks and Heterogeneous Media, 2013, 8 (2) : 433-463. doi: 10.3934/nhm.2013.8.433
[15]

Michael Herty, S. Moutari, M. Rascle. Optimization criteria for modelling intersections of vehicular traffic flow. Networks and Heterogeneous Media, 2006, 1 (2) : 275-294. doi: 10.3934/nhm.2006.1.275
[16]

Yunxiang Han, Xiaoqiong Huang. Traffic flow modeling and optimization control in the approach airspace. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022109
[17]

Guillaume Costeseque, Jean-Patrick Lebacque. Discussion about traffic junction modelling: Conservation laws VS Hamilton-Jacobi equations. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 411-433. doi: 10.3934/dcdss.2014.7.411
[18]

Emiliano Cristiani, Fabio S. Priuli. A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks. Networks and Heterogeneous Media, 2015, 10 (4) : 857-876. doi: 10.3934/nhm.2015.10.857
[19]

Gabriella Bretti, Maya Briani, Emiliano Cristiani. An easy-to-use algorithm for simulating traffic flow on networks: Numerical experiments. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 379-394. doi: 10.3934/dcdss.2014.7.379
[20]

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

2021 Impact Factor: 1.41

Tools

Metrics

  • PDF downloads (71)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy