  Wireless sensor networks (WSNs) are becoming increasingly utilized in
applications that require remote collection of data on environmental
conditions. In particular dense WSNs are emerging as an important sensing
platforms for the Internet of Things (IoT). WSNs are able to generate huge
volumes of raw data, which require network structuring and efficient
collaboration between nodes to ensure efficient transmission. In order to
reduce the amount of data carried in the network, data aggregation is used in
WSNs to define a policy of data fusion and compression. In this paper, we
investigate a model for data aggregation in a dense {WSN} with a single sink.
The model divides a circular coverage region centered at the sink into patches
which are intersections of sectors of concentric rings, and data in each patch
is aggregated at a single node before transmission. Nodes only communicate with
other nodes in the same sector. Based on these assumptions, we formulate a
linear programming problem to maximize system lifetime by minimizing the
maximum proportionate energy consumption over all nodes. Under a wide variety
of conditions, the optimal solution employs two transmissions mechanisms:
direct transmission, in which nodes send information directly to the sink; and
stepwise transmission, in which nodes transmit information to adjacent nodes.
An exact formula is given for the proportionate energy consumption rate of the
network. Asymptotic forms of this exact solution are also derived, and are
verified to agree with the linear programming solution. We investigate three
strategies for improving system lifetime: nonuniform energy and information
density; iterated compression; and modifications of rings. We conclude that
iterated compression has the biggest effect in increasing system lifetime.
