The numerical solution for the optimal
d is plotted as a function of c in Figure 2(b). This figures quantifies the
insight that a smaller look-ahead (corresponding to a trajectory based search)
is favored when the environmental dynamics are so high that caching is not
e?®ective (high c), whereas a larger look-ahead (resembling flooding) is favored
when caches can be used with high frequency (low c).
3 Cluster-Based Joint Routing and Compression
Because of their application-specificity, sensor networks are capable of performing
data-centric routing, which allows for in-network processing of information.
In particular, to reduce total energy consumption, data from correlated
sensors can be compressed at intermediate nodes even as they are
routed. We examine now how the appropriate joint routing and compression
strategy can depend on the degree of correlation between the sources.
We first need a model to quantify the amount of information generated by
a set of sources.We use here a simple model that has been previously validated
with some real data [3]. In this model, there is a tunable parameter ?± which
varies from 0 to 1 and provides an indicator of the level of correlation between
the sources. We use the joint entropy Hn of the sources as the measure of the
total information they generate, assuming that each individual source has an
identical entropy of H1:
Hn(?±) = H1(1 + ?±(n ??’ 1)). (4)
Thus, when ?± = 0, the correlation is the highest (the sources sensing
identical readings), resulting in a joint entropy that is equal to the entropy
391
Bhaskar Krishnamachari
(a)
(b)
Fig.
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