Journal of Applied Probability
- J. Appl. Probab.
- Volume 53, Number 3 (2016), 833-845.
Bounded-hop percolation and wireless communication
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.
J. Appl. Probab. Volume 53, Number 3 (2016), 833-845.
First available in Project Euclid: 13 October 2016
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
Hirsch, Christian. Bounded-hop percolation and wireless communication. J. Appl. Probab. 53 (2016), no. 3, 833--845.https://projecteuclid.org/euclid.jap/1476370779