## Bernoulli

- Bernoulli
- Volume 22, Number 4 (2016), 2143-2176.

### Connection times in large ad-hoc mobile networks

Hanna Döring, Gabriel Faraud, and Wolfgang König

#### Abstract

We study connectivity properties in a probabilistic model for a large mobile ad-hoc network. We consider a large number of participants of the system moving randomly, independently and identically distributed in a large domain, with a space-dependent population density of finite, positive order and with a fixed time horizon. Messages are instantly transmitted according to a relay principle, that is, they are iteratively forwarded from participant to participant over distances smaller than the communication radius until they reach the recipient. In mathematical terms, this is a dynamic continuum percolation model.

We consider the connection time of two sample participants, the amount of time over which these two are connected with each other. In the above thermodynamic limit, we find that the connectivity induced by the system can be described in terms of the counterplay of a local, random and a global, deterministic mechanism, and we give a formula for the limiting behaviour.

A prime example of the movement schemes that we consider is the well-known random waypoint model. Here, we give a negative upper bound for the decay rate, in the limit of large time horizons, of the probability of the event that the portion of the connection time is less than the expectation.

#### Article information

**Source**

Bernoulli, Volume 22, Number 4 (2016), 2143-2176.

**Dates**

Received: January 2015

Revised: March 2015

First available in Project Euclid: 3 May 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1462297678

**Digital Object Identifier**

doi:10.3150/15-BEJ724

**Mathematical Reviews number (MathSciNet)**

MR3498026

**Zentralblatt MATH identifier**

1343.60136

**Keywords**

ad-hoc networks connectivity dynamic continuum percolation large deviations random waypoint model

#### Citation

Döring, Hanna; Faraud, Gabriel; König, Wolfgang. Connection times in large ad-hoc mobile networks. Bernoulli 22 (2016), no. 4, 2143--2176. doi:10.3150/15-BEJ724. https://projecteuclid.org/euclid.bj/1462297678