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In-Depth Information
Probabilistics routing in an area of 200
×
200 in metre square
200
1
2
0
1
0
Nodes
Paths b/w nodes
4
5
3
4
4
8
180
2
2
6
4
7
160
1
8
3
4
2
7
2
4
49
1
1
3
2
140
41
1
5
1
7
2
5
40
120
3
3
4
3
100
5
3
1
3
7
1
6
2
1
50
80
1
3
1
4
60
1
2
9
2
8
2
9
30
8
339
40
3
3
6
1
4
2
3
6
20
2
2
4
6
2
7
4
4
0
0
20
40
60
80
100
120
140
160
180
200
Distance in X-axis in metres
Fig. 7.12
Probabilistic model showing next forwarding hops (
s
= 8 dB) in an area of 200 × 200 m
2
7.8
Simulation results
In running the simulations we vary the following parameters:
Parameter 1
: Shadowing correlation length to equivalent UDG transmission
radius ratio, defined as
d
shadow fading 50% de - correlation distance
ψ =
=
50%
.
equivalent UDG radius (
d
for which
ppr
=
0.5)
R
This parameter, schematically shown in Fig.
7.13
determines whether the
correlated shadow fading
ppr
contour “amoeba” has many protrusions/legs (low
value of
y
) or few such features (high value of
y
).
Parameter 2
: Average node density, defined as
average number of neighbouring nodes for which
ppr
≥
threshold
=
0.5
.
k
=
UDG area
The average node density is controlled by varying the number of nodes and the
size of the simulation area. The values employed in the simulations were an area of
400 × 400 m
2
with 100, 125, 135, 150, 200, 250, 275, and 300 nodes and an area
of 500 × 500 m
2
with 250, 275, 300, and 350 nodes. For every such simulation, 12
independent realizations were chosen in order to ensure that statistically meaningful
hop count data were collected.
Parameter 3
: Shadow fading standard deviation,
d
σ
. This was chosen to take
values of 0 dB (an extreme case of no fading where propagation and
ppr
are
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