On the Critical Transmission Range in
One-Dimensional
Sensor Networks Under Non-Uniform Node Placement
Professor Armand M. Makowski
Department of Electrical and
Computer Engineering and
the Institute for Systems Research
University of Maryland, College Park,
MD 20742
armand@isr.umd.edu
We consider n sensors
independently placed at points X1,...,Xn on the
unit interval[0,1]according to some probability distribution
function F. Two sensor nodes communicate with each other if
their distance is less than some given transmission range ρ > 0. We deŽne the
critical transmission range Rn as the
smallest transmission range such that the nodes X1,...,Xn form a
connected graph (under the notion of adjacency implied by the ability of nodes
to communicate). Since the distribution of Rn is usually not tractable, we are interested in
developing an asymptotic theory for Rn as n
becomes large: We seek a
deterministic sequence ρ* :
N0 → R+ such
that the ratio Rn/ρn⋆ converges to some
non-trivial limit L in an appropriate sense. When available, such
results suggest ρ⋆n L as a proxy or approximation for Rn.
We assume that F
admits a continuous density f,
and two qualitatively different cases are identiŽed, namely f ⋆
> 0
and f⋆
= 0 with f⋆
= inf(f(x),x ∈
[0,1]). In each case, we present results on the form
of ρ*n and
L. In the process we make contact
with the existence and nature of critical thresholds for the property of graph
connectivity in the underlying geometric random graph. Engineering implications
for power allocation are discussed.
Wednesday, August 26, 2009 3-4 pm Room 1200 EECS
This is joint work with former Ph.D. student Guang Han (now at
Motorola).