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.
Similar content being viewed by others
References
Baccelli, F., Błaszczyszyn, B.: Stochastic Geometry and Wireless Networks. Foundation and Trends in Networking Series. NOW Publishers (2009).
Feller, W.: An Introduction to Probability Theory and its Applications. Vol. II. Wiley, New York (1970)
Haenggi, M., Ganti, R.K.: Interference in Large Wireless Networks. Foundation and Trends in Networking Series. NOW Publishers (2009).
Nguyen, V.M., Baccelli, F.: A stochastic geometry model for the best signal quality in a wireless network. In: Proceedings of the 8th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt) (2010)
Stoyan, D., Stoyan, H.: On one of Matérn’s hard core point process models. Math. Nachr. 122, 205–214 (1985)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Baccelli, F., Bermolen, P. Extremal versus additive Matérn point processes. Queueing Syst 71, 179–197 (2012). https://doi.org/10.1007/s11134-012-9280-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11134-012-9280-3
Keywords
- Stochastic geometry
- Additive shot noise process
- Extremal shot noise process
- Point process with repulsion