Journal of Applied Probability

Bounded-hop percolation and wireless communication

Christian Hirsch

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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.

Article information

Source
J. Appl. Probab. Volume 53, Number 3 (2016), 833-845.

Dates
First available in Project Euclid: 13 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1476370779

Mathematical Reviews number (MathSciNet)
MR3570097

Zentralblatt MATH identifier
1351.60127

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Keywords
Ad hoc network chemical distance connection probability continuum percolation

Citation

Hirsch, Christian. Bounded-hop percolation and wireless communication. J. Appl. Probab. 53 (2016), no. 3, 833--845.https://projecteuclid.org/euclid.jap/1476370779


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