Modeling for Geo-Routing in Multi-Hop Wireless Networks - Application and Multidisciplinary Aspects of Wireless Sensor Networks - page 154

represented by cyan) then forwards the data to node “'25,” as it is closest to the
destination (node “50”), and so on.
The two parameters that have been calculated for the Dijkstra and UDG models
are the “ Network Density ” and the “ Hop Count. ” Network density is defined as the
average number of neighbors per each node that lies within the transmission radius
of each node and is found to be 9.72 nodes per UDG area for both UDG and
Dijkstra models, since the transmission radius of both is chosen on the basis of
receiver sensitivity. Hop count is defined as the number of hops taken to reach from
source to destination and is found to be 4 (Figs. 7.6 and 7.8 ) for both the Dijkstra
and UDG models.

7.7.1 Probabilistic Model When Standard Deviation ( s )

of Shadow Fading is Zero

In this section, the standard deviation of the shadow fading is taken to be zero,
which means that the shape of the transmission range will be circular, but still
follows the same functionality as defined in pseudo code to find the neighboring
nodes and the forwarding hop is chosen on the basis of probabilistic greedy algo-
rithm. With s = 0 there is no shadow fading and the probabilistic greedy algorithm
works only on the median path loss and the plots of the “ ppr ” against distance is
given in Fig. 7.1a .
Figure 7.1a shows the distance that can be included in the transmission range
which is around 64 m when the ppr is taken to be 0.5 with s = 0. The plot shown
below shows the path that has been chosen by the probabilistic greedy algorithm
for the example of 50 nodes in an area of 200 × 200 m 2 :
The network node density in this case is 10.36 nodes per UDG area and the hop
count is 5 (Fig. 7.10 ).

7.7.2 Proposed Model When Standard Deviation ( s ) of Shadow

Fading is Six Decibels

In this section, the standard deviation of the shadow fading is taken to be 6 dB and
follows the same functionality as defined in pseudo code to find the neighboring
nodes and the forwarding hop is chosen on the basis of probabilistic greedy
algorithm. The path followed from source to destination is given below:
The two metrics that have been calculated on the proposed model with s = 6 dB
are the “ Network Density ” and the “ Hop Count. ” The network node density in this
case is 11.42 nodes per UDG area and the hop count is 4 (Fig. 7.11 ).