Lattice Green functions and diffusion for modelling traffic routing in ad hoc networks

Marc Sigelle; Ian Jermyn; Sylvie Perreau; Aruna Jayasuriya

2nd International Workshop on Physics-Inspired Paradigms in Wireless Communications and Networks

Research Article

Lattice Green functions and diffusion for modelling traffic routing in ad hoc networks

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.1109/WIOPT.2009.5291591,
    author={Marc Sigelle and Ian Jermyn and Sylvie Perreau and Aruna Jayasuriya},
    title={Lattice Green functions and diffusion for modelling traffic routing in ad hoc networks},
    proceedings={2nd International Workshop on Physics-Inspired Paradigms in  Wireless Communications and Networks},
    publisher={IEEE},
    proceedings_a={PHYSCOMNET},
    year={2009},
    month={10},
    keywords={ad hoc networks Laplace-Beltrami operator Green functions random walks traffic propagation},
    doi={10.1109/WIOPT.2009.5291591}
}

Marc Sigelle
Ian Jermyn
Sylvie Perreau
Aruna Jayasuriya
Year: 2009
Lattice Green functions and diffusion for modelling traffic routing in ad hoc networks
PHYSCOMNET
IEEE
DOI: 10.1109/WIOPT.2009.5291591

Marc Sigelle¹^,*, Ian Jermyn²^,*, Sylvie Perreau³^,*, Aruna Jayasuriya³^,*

1: Institut TELECOM TELECOM ParisTech CNRS UMR 5141, 46 rue Barrault, 75634 Paris Cedex 13, France
2: Ariana research group (INRIA/I3S), INRIA, 2004 route des Lucioles, 06902 Sophia Antipolis Cedex, France
3: Institute for Telecommunications Research, University of South Australia Mawson Lakes, Adelaide Australia

*Contact email: marc.sigelle@telecom-paristech.fr, ian.jermyn@sophia.inria.fr, sylvie.perreau@unisa.edu.au, aruna.jayasuriya@unisa.edu.au

Abstract

We describe basic properties of Markov chains on finite state spaces and their application to Green functions, partial differential equations, and their (approximate) solution using random walks on a graph. Attention is paid to the influence of boundary conditions (Dirichlet/von Neumann). We apply these ideas to the study of traffic propagation and distribution in adhoc networks.

Keywords: ad hoc networks Laplace-Beltrami operator Green functions random walks traffic propagation

Published: 2009-10-23
Publisher: IEEE
Modified: 2010-05-16

: http://dx.doi.org/10.1109/WIOPT.2009.5291591