  In this paper we analyze the trade-offs between energy and throughput for
links in a wireless sensor network. Our application of interest is one in which
a number of low-powered sensors need to wirelessly communicate their
measurements to a communications sink, or destination node, for communication
to a central processor. We focus on one particular sensor source, and consider
the case where the distance to the destination is beyond the peak power of the
source. A relay node is required. Transmission energy of the sensor and the
relay can be adjusted to minimize the total energy for a given throughput of
the connection from sensor source to destination. We introduce a bounded random
walk model for movement of the relay between the sensor and destination nodes,
and characterize the total transmission energy and throughput performance using
Markov steady state analysis. Based on the trade-offs between total energy and
throughput we propose a new time-sharing protocol to exploit the movement of
the relay to reduce the total energy. We demonstrate the effectiveness of
time-sharing for minimizing the total energy consumption while achieving the
throughput requirement. We then show that the time-sharing scheme is more
energy efficient than the popular sleep mode scheme.
