A wireless sensor network (WSN) with multiple sinks can be divided into subnetworks, each of which is composed of a single sink, data sources reporting to the sink, and sensors relaying messages for the sources. Sensors that appear in more than one such subnetwork will consume energy for all their participating subnetworks. Hence, without loss of generality, we investigate theoretical aspects of the energy hole problem, that is, the uneven energy depletion phenomenon, in single-sink WSNs. We will establish power consumption models for sensor-to-sink communication.

Because exact energy usage prediction is not possible due to network diversity, uncertainty, and dynamics, the models to be presented below are obtained through reasonable approximation. We first present network models and assumptions; then we establish the energy consumption models in two different network scenarios, where sensors have fixed or variable transmission radius respectively. For these two scenarios, we also show how to balance energy usage by applying nonuniform sensor distribution or adjustable transmission radii. The content of this section is based on Olariu and Stojmenovic (2006).

6.2.1 Network Model and Assumptions

Denote by Et(d) the amount of energy consumed by the sender for transmitting one data bit to distance d, and by Er the amount of energy spent by receiver in receiving one data bit. The total cost of transmitting one data bit between sender and receiver in one hop is ...

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