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a
b
low value of
y
high value of
y
c
ψ
;
1
Fig. 7.13
Typical
ppr
contours (
solid lines
) for (
a
) a low value of
ψ
, (
b
) a high value of
1
ψ≤
, the ratio
y
acquires the geometrical explanation of being approximately equal to the
angle in radians, as observed at the transmitting node, of the “typical width” of its regions, where
d
>
d
50%
=
R
= 70 m for its
ppr
= 0.5 contour, since
1
(
c
) For
1
c
ψ
=
LR
/
=
2sin
1
2
ϕ ϕ ϕ≤
(maxi
»
for
mum error of 4%)
deterministic functions of distance from the transmitter), 6 and 8 dB, which are the
typical reported values in [
4
].
The simulations are performed as follows: The source node is always chosen to
be the node with the minimum xcoordinate value and the destination node is
always chosen to be the node with the maximum xcoordinate value throughout the
simulations. The average hop count over 12 independent network topology realiza
tions per node density is computed, together with standard error bars to show the
spread of values. The results of the simulations are shown in Figs.
7.14

7.16
. The
greedy algorithm has a hop count close to the optimal (found by Dijkstra's
algorithm); local knowledge prevents it from finding always an optimal path, and
sometimes it does not find a path at all in a connected network. Furthermore, the
performance of the unrealistic
=σ
model is,
on average
, expected to be the
same as that of the greedy algorithm on UDG and this is in good agreement with
the results of Figs.
7.14

7.16
given that only 12 ensemble realizations are used to
compute averages.
It is clear from the simulations that there exist certain combinations of values of
y
,
k
and
d
σ
, where the performance of the probabilistic progress localized routing
algorithm with a realistic physical layer is significantly better than the corresponding
performance predicted by greedy algorithm applied on both the UDG and the
unrealistic
0 dB
dB
σ
=
0 dB
models.
dB
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