(7)
393
Bhaskar Krishnamachari
Fig. 3. Illustrative Scenario for Cluster-based Routing with Compression.
The minimization of the above expression for the total cost yields the
optimal cluster size to be
sopt(?±) = r2D
1 ??’ ?±
?±
. (8)
The above applies for all intermediate values of ?± in (0, 1). For the two
extreme cases, we get that when ?± = 0, sopt(0) = n and when ?± = 1, sopt = 1.
Figure 4(a) shows the performance for di?®erent cluster sizes as a function of
the correlation level, for a scenario with n = 100,D = 100. Figure 4(b) shows
the optimal cluster size sopt decreasing with ?±. This quantifies the tradeo?®
mentioned above, that a high correlation favors large clusters, while low correlations
favor small clusters.
In [3], this analysis is validated for more general topologies through simulations
involving random placement of sensors in a 2D region. Another interesting
finding of that study is that while the optimal cluster size is indeed
a function of the level of correlation, it is also possible to use a static cluster
size that provides near-optimal performance regardless of the correlation.
While we do not go into the analysis of the near-optimal clustering here, it is
interesting to note that Figure 4(a) suggests such a result ??” the cluster size
of 20 provides good performance for all correlation levels.
4 Joint Search and Replication
As a third case study to illustrate first-order modeling, we examine the problem
of querying a sensor network for information that can be replicated.
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