American Institute of Mathematical Sciences

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September  2007, 2(3): 497-528. doi: 10.3934/nhm.2007.2.497

Equilibria for data networks

Alessia Marigo 1,

1. 

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

Received  February 2007 Revised  May 2007 Published  June 2007

This paper investigates equilibrium solutions for data flows on a network. We consider a fluid dynamic model based on conservation laws. The dynamics at nodes is solved by FIFO policy combined with through flux maximization. We first link the dimension of the equilibria space to topological properties of the graph associated to the network. Then we focus on regular plane tilings with square or triangular cells. For various networks, we completely determine the characteristics of periodic equilibria and, in some cases, of all equilibria. The obtained results are expected to play a role both in the analysis of asymptotic behavior of network load and for security issues in case of node failures.
Keywords: Traffic on Networks, Equilibria.
Mathematics Subject Classification: Primary: 90B18; Secondary: 35L6.
Citation: Alessia Marigo. Equilibria for data networks. Networks & Heterogeneous Media, 2007, 2 (3) : 497-528. doi: 10.3934/nhm.2007.2.497
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