Random Distances Associated with Hexagons
arXiv:1106.2200
Abstract
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. The first two statistical moments of the random distances, and the polynomial fits of the density functions are also given in this report for practical uses.
brief results announcement, based on arXiv:1106.1257; a calculation error in (15) has been corrected (changes in red)
References in corpus (1)
Cited by in corpus (6)
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- The moments of the distance between two random points in a regular polygon
- Errata and Addenda to Mathematical Constants