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Conditional length distributions induced by the coverage of two points by a Poisson Voronoï tessellation: application to a telecommunication model
Author(s) -
Gloaguen Catherine
Publication year - 2006
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.630
Subject(s) - poisson distribution , tessellation (computer graphics) , poisson process , poisson point process , euclidean geometry , mathematics , point process , distribution (mathematics) , simple (philosophy) , computer science , statistical physics , combinatorics , statistics , geometry , mathematical analysis , physics , philosophy , epistemology
The end points of a fixed segment in the Euclidian plane covered by a Poisson Voronoï tessellation belong to the same cell or to two distinct cells. This marks off one or two points of the underlying Poisson process that are the nucleus(i) of the cell(s). Our interest lies in the geometrical relationship between these nuclei and the segment end points as well as between the nuclei. We investigate their probability distribution functions conditioning on the number of nuclei, taking into account the length of the segment. The aim of the study is to establish some tools to be used for the analysis of a telecommunication problem related to the pricing of leased lines. We motivate and give accurate approximations of the probability of common coverage and of the length distributions that can be included in spreadsheet codes as an element of simple cost functions. Copyright © 2006 John Wiley & Sons, Ltd.