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low value of y
high value of y
ψ ;
Fig. 7.13 Typical ppr contours ( solid lines ) for ( a ) a low value of
ψ , ( b ) a high value of
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
( c ) For
1 c
ϕ ϕ ϕ≤ (maxi-
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 x-coordinate value and the destination node is
always chosen to be the node with the maximum x-coordinate 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
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
0 dB
0 dB
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