Abstract: Sensor networks are made of autonomous devices that are able to
collect, store, process and share data with other devices. Large sensor
networks are often redundant in the sense that the measurements of some nodes
can be substituted by other nodes with a certain degree of confidence. This
spatial correlation results in wastage of link bandwidth and energy. In this
paper, a model for two associated Poisson processes, through which sensors are
distributed in a plane, is derived. A probability condition is established for
data redundancy among closely located sensor nodes. The model generates a
spatial bivariate Poisson process whose parameters depend on the parameters of
the two individual Poisson processes and on the distance between the associated
points. The proposed model helps in building efficient algorithms for data
dissemination in the sensor network. A numerical example is provided
investigating the advantage of this model.