Propagation properties for a message in a Brownian sensor network

Niklas  Gunnarsson; Ingemar  Kaj; Petteri  Mannersalo

Second Workshop on Spatial Stochastic Models for Wireless Networks

Research Article

Propagation properties for a message in a Brownian sensor network

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.1109/WIOPT.2006.1666520,
    author={Niklas  Gunnarsson and Ingemar  Kaj and Petteri  Mannersalo},
    title={Propagation properties for a message in a Brownian sensor network},
    proceedings={Second Workshop on Spatial Stochastic Models for Wireless Networks},
    publisher={IEEE},
    proceedings_a={SPASWIN},
    year={2006},
    month={8},
    keywords={},
    doi={10.1109/WIOPT.2006.1666520}
}

Niklas Gunnarsson
Ingemar Kaj
Petteri Mannersalo
Year: 2006
Propagation properties for a message in a Brownian sensor network
SPASWIN
IEEE
DOI: 10.1109/WIOPT.2006.1666520

Niklas Gunnarsson¹^,*, Ingemar Kaj²^,*, Petteri Mannersalo³^,*

1: Dept. of Mathematics, Uppsala University, Box 480 SE 751 06 Uppsala, Sweden,
2: Dept. of Mathematics, Uppsala University, Box 480 SE 751 06 Uppsala, Sweden
3: VTT Technical Research, Centre of Finland, P.O.Box 1000, 02044 VTT, Finland

*Contact email: niklas@math.uu.se, ikaj@math.uu.se, petteri.mannersalo@vtt.fi

Abstract

A wireless multi-hop sensor network, in which node positions are fixed, may fail to transmit a message over longer distances. This could occur, for example, due to low node density or small node transmission range. In mobile systems where nodes are allowed to move, it is natural to expect a better reachability, with the condition that messages are not time-critical and longer propagation delays are permitted. In order to understand the relation of mobility to node density and node transmission range, we study a simple network model where active sensors move according to independent Brownian motions. In the one-dimensional case, the propagation of a message can be viewed as a Brownian growth process among Poisson points on the real line. We investigate the distributional properties of the mobile nodes and show that the system grows linearly at a remarkably uniform rate. For the spatial model where planar Brownian motions transport and transfer the message to those nodes which eventually come within transmission range of active messenger nodes, we provide a discussion and some insight based primarily on simulations.

Published: 2006-08-07
Publisher: IEEE

: http://dx.doi.org/10.1109/WIOPT.2006.1666520