On placement of multiple sinks in wireless sensor networks

A primary task in wireless sensor networks (WSNs) is for sensors to communicate collected data to a sink for analysis and processing. A single sink in the network can lead to high energy consumption and hence, a reduction of the network lifetime. Thus, to achieve a degree of fault tolerance we consider the problem, where the hop distance from every sensor to a sink is bounded by an integer k and each sensor is within distance k of r sinks. This problem is equivalent to a distance-k total r-dominating set, denoted D
_{k, r}
, in WSNs. Due to generally large number of sensors in WSNs or the network being constructed in an unreachable terrain, sensors may be arranged stochastically. Because of this uncertainty and randomness in the network structure, WSNs can be modelled as random graphs. In this work, we study upper bounds on the size of D
_{k, r}
, where a WSN is modelled as a random graph.