This paper develops a stochastic model for data in a Wireless Sensor Network using random field theory. The model captures the space-time behavior of the underlying phenomenon being observed by the network. We then study the size and spatial distribution of the regions of the network that sense statistically extreme values using the theory of extreme excursion regions. Analytical expressions are found for the average size of the data load in a variety of scenarios. These expressions compliment many existing works in the literature that describe algorithms to reduce the data load but cannot evaluate the size and spatial distribution of this load except through simulation. We show that if only the statistically extreme data is transmitted in the network, then the data load can be significantly reduced. Analytical expressions for the total data load are confirmed with simulation. Finally, a simple performance model of a WSN is developed based on a collection of asynchronous M/M/1 servers working in parallel. We derive several performance measures from this performance model. The presented results will be useful in the design of large scale sensor networks.
['Glenn Patterson', 'Mustafa K. Mehmet Ali']
Modeling of Extreme Data in Wireless Sensor Networks