Modelling of extreme data in a Wireless Sensor Network through the application of random field theory

Wireless Sensor Networks (WSNs) consist of a large number of small, simple sensor nodes which support sensing, processing, and wireless transmission capabilities in order to monitor some physical environment. The data that they collect will be transmitted to an information sink where it can be accessed by the user. Due to the vast number of nodes expected in many WSN applications, there is the possibility that at certain times the network may have potentially huge amounts of data to transmit to the sink. The fact that the nodes have limited energy resources means that when a huge amount of data is generated, the nodes' batteries will be depleted at aggressive rates as nodes try to forward this data to the sink. This problem will be particularly severe in regions of the network close to the sink, as nodes in these regions will be responsible for routing the data from large areas of the network to the sink. This phenomenon is often described as a "data-implosion" around the sink. We develop a model of the node data in a wireless sensor network based on a stochastic model of the underlying phenomenon being observed by the network. The model is based on a stationary Gaussian random field and we use this model to study the size and spatial distribution of the sets of nodes that observe statistically high data. This knowledge is exploited in order to ameliorate the data-implosion problem. Effectively, we implement a data suppression scheme that only lets nodes which sense statistically high data attempt to transmit their data to the sink. Further, we also use our model to study network data that belongs to a given contour level and show that we can achieve further data suppression by only transmitting node data if it belongs to some predefined contour level. Finally, we show how the knowledge of the size and spatial distribution of statistically high node data in a WSN can be used to study the traffic in both schedule and contention based MAC protocols.