Connection times in large ad-hoc mobile networks

TL;DR

This paper analyzes the connectivity duration between two nodes in large mobile ad-hoc networks using a probabilistic continuum percolation model, revealing the interplay of local randomness and global structure affecting connection times.

Contribution

It introduces a mathematical framework for understanding connection times in large mobile networks, especially under the random waypoint movement scheme, with explicit formulas for asymptotic behavior.

Findings

Connectivity can be described by local and global mechanisms.

Provided a formula for the limiting connection time behavior.

Established bounds on the decay rate of connection probability.

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.