Protocols for Secure Communication in Wireless Sensor Networks

148 Chapter 5. Multipath Communication
5.3.4 Delivery Rate
Figure 5.11: Distribution of out-degree
As discussed above, the convex hull created from the cover areas of a set of
nodes may contain locations that are actually not in the cover area of any of
these nodes. Thus, a message may be routed to a subtree that does not contain
any node covering the target location of the message. The delivery rate depends
on the topology of the network and the cover density, i.e. the number of nodes
whose cover area contains a certain location.
Figure 5.12 shows the increase of the delivery rate when the cover area of
single node is increased. It seems clear that a nearly full delivery rate, for
example r > 0.99, cannot be achieved practically. The reason is that this would
require a cover area per node that is very large compared to the size of the
deployment area. For high precision of results, and low resource usage, it is
best to keep the cover area small.
An increase node density d, which denotes the average number of neighbours
of each node, leads to a larger number of subtrees in each node as the
tree construction favours shallow trees. This causes the available cover nodes
to be distributed among a larger number of subtrees, thereby reducing the probability
that a cover node is contained in a subtree.
Figure 5.13 shows that an increased cover density has the same effect on
graphs whose topology is determined by the Gabriel graph. However, using
the Gabriel construction, the topology is invariant to changes in node density.
Therefore, node density shows little to no effect in the simulation results.