Random Distances Associated with Hexagons

Understand

In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent hexagons sharing a side, respectively.

• Simulation results show the accuracy of the obtained closed-form distance distribution functions, which are important in a wide variety of applied sciences and engineering fields.
• In particular, hexagons are often used in wireless communication networks such as the cellular systems.
• The correctness of these distance distribution functions is validated by a recursion and a probabilistic sum.