  In trying to emulate the spatial position of wireless nodes for purpose of
analysis, we rely on stochastic simulation. And, it is customary, for mobile
systems, to consider a base-station radiation coverage by an ideal cell shape.
For cellular analysis, a hexagon contour is always preferred mainly because of
its tessellating nature. Despite this fact, largely due to its intrinsic
simplicity, in literature only random dispersion model for a circular shape is
known. However, if considered, this will result an unfair nodes density
specifically at the edges of non-circular contours. As a result, in this paper,
we showed the exact random number generation technique required for nodes
scattering inside a hexagon. Next, motivated from a system channel perspective,
we argued the need for the exhaustive random mobile dropping process, and hence
derived a generic close-form expression for the path-loss distribution density
between a base-station and a mobile. Last, simulation was used to reaffirm the
validity of the theoretical analysis using values from the new IEEE 802.20
standard.
