Superposition of planar voronoi tessellations

We study the tessellation obtained in the intersection of two independent planar Poisson-Voronoi tessellations and derive the means of its main geometrical characteristics. We distinguish six types of cell depending on the position of nuclei of the original tessellations. The intensity and the mean area of each type of cell are computed either in closed form or via asymptotic expansions. The model can be used to represent different types of local zones of two competing telecommunication operators where the interconnection of two subscribers induces a specific cost within each type of zone