The Boolean Model

In mobile communications, one often encounters marked point processes. For example, we can associate the random set M_n with each point X_n of the point process $X=\{X_1,X_2,\ldots\}$.Then, the shifted set M_n + X_n can be interpreted for example as the random range of the station at location X_n. One of the quantities of main interest is the union of these sets and its characteristics, e.g. the probability that an arbitrary point is covered by this union. This leads to the notion of the Boolean model.