Translator Disclaimer
September 2016 Bounded-hop percolation and wireless communication
Christian Hirsch
Author Affiliations +
J. Appl. Probab. 53(3): 833-845 (September 2016).

Abstract

Motivated by an application in wireless telecommunication networks, we consider a two-type continuum-percolation problem involving a homogeneous Poisson point process of users and a stationary and ergodic point process of base stations. Starting from a randomly chosen point of the Poisson point process, we investigate the distribution of the minimum number of hops that are needed to reach some point of the base station process. In the supercritical regime of continuum percolation, we use the close relationship between Euclidean and chemical distance to identify the distributional limit of the rescaled minimum number of hops that are needed to connect a typical Poisson point to a point of the base station process as its intensity tends to 0. In particular, we obtain an explicit expression for the asymptotic probability that a typical Poisson point connects to a point of the base station process in a given number of hops.

Citation

Download Citation

Christian Hirsch. "Bounded-hop percolation and wireless communication." J. Appl. Probab. 53 (3) 833 - 845, September 2016.

Information

Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1351.60127
MathSciNet: MR3570097

Subjects:
Primary: 60K35
Secondary: 60D05

Keywords: Ad hoc network , Chemical distance , connection probability , continuum percolation

Rights: Copyright © 2016 Applied Probability Trust

JOURNAL ARTICLE
13 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.53 • No. 3 • September 2016
Back to Top