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Queueing Systems

, Volume 71, Issue 1–2, pp 179–197 | Cite as

Extremal versus additive Matérn point processes

  • François BaccelliEmail author
  • Paola Bermolen
Article

Abstract

In the simplest Matérn point processes one retains certain points of a Poisson point process in such a way that no pairs of points are at distance less than a threshold. This condition can be reinterpreted as a threshold condition on an extremal shot–noise field associated with the Poisson point process. This paper is focused on the case where one retains points that satisfy a threshold condition based on an additive shot–noise field of the Poisson point process. We provide an analytical characterization of the intensity of this class of point processes and we compare the packing obtained by the extremal and additive schemes and certain combinations thereof.

Keywords

Stochastic geometry Additive shot noise process Extremal shot noise process Point process with repulsion 

Mathematics Subject Classification (2000)

60-XX 

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References

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.INRIA and Ecole Normale SupérieureLINCSParisFrance
  2. 2.Universidad de la RepúblicaMontevideoUruguay

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