Numerical solutions of continuum equilibria for routing in dense ad-hoc networks

Alonso Silva; Eitan Altman; Pierre Bernhard

3rd International ICST Workshop on Interdisciplinary Systems Approach in Performance Evaluation and Design of Computer & Communication Systems

Research Article

Numerical solutions of continuum equilibria for routing in dense ad-hoc networks

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.4108/ICST.VALUETOOLS2008.4521,
    author={Alonso Silva and Eitan Altman and Pierre Bernhard},
    title={Numerical solutions of continuum equilibria for routing in dense ad-hoc networks},
    proceedings={3rd International ICST Workshop on Interdisciplinary Systems Approach in Performance Evaluation and Design of Computer \& Communication Systems},
    publisher={ACM},
    proceedings_a={INTER-PERF},
    year={2010},
    month={5},
    keywords={Wireless Ad-Hoc Networks Wireless Sensor Networks Wardrop Equilibrium Finite Element Methods},
    doi={10.4108/ICST.VALUETOOLS2008.4521}
}

Alonso Silva
Eitan Altman
Pierre Bernhard
Year: 2010
Numerical solutions of continuum equilibria for routing in dense ad-hoc networks
INTER-PERF
ICST
DOI: 10.4108/ICST.VALUETOOLS2008.4521

Alonso Silva¹^,*, Eitan Altman¹^,*, Pierre Bernhard²^,*

1: INRIA, 2004 Route des Lucioles, B.P. 93, 06902 Sophia-Antipolis, Cedex, France
2: I3S, Université de Nice-Sophia, Antipolis and CNRS, 940 Route des Colles, B.P. 145, 06903 Sophia-Antipolis, Cedex, France

*Contact email: alonso.silva@inria.fr, eitan.altman@inria.fr, pierre.bernhard@polytech.unice.fr

Abstract

We study the routing problem in massively dense static ad-hoc networks as the node density increases. We use a fluid approximation in which the graph providing the available routes becomes so dense that it can be approximated by a continuous area which inherits from the original problem the cost structure: a cost density is defined at each point on the limit plain; it is a function of the location and the congestion at that point. We solve numerically the routing problem for the case where the cost density is linear with respect to congestion and we obtain a result of convergence via Finite Elements Method.

Keywords: Wireless Ad-Hoc Networks Wireless Sensor Networks Wardrop Equilibrium Finite Element Methods

Published: 2010-05-16
Publisher: ACM
Modified: 2010-05-16

: http://dx.doi.org/10.4108/ICST.VALUETOOLS2008.4521