Probabilistic Modelling of Information Propagation in Wireless Mobile Ad-Hoc Network

In this paper the dynamics of broadcasting wireless ad-hoc networks is studied through probabilistic modelling. A randomized transmission discipline is assumed in accordance with existing MAC definitions such as WLAN with Decentralized Coordination or IEEE-802.15.4. Message reception is assumed to be governed by node power-down policies and is equivalently assumed to be randomized. Altogether randomization facilitates a probabilistic model in the shape of an integro-differential equation governing the propagation of information, where brownian node mobility may be accounted for by including an extra diffusion term. The established model is analyzed for transient behaviour and a travelling wave solution facilitates expressions for propagation speed as well as parametrized analysis of network reliability and node power consumption. Applications of the developed models for node localization and network dimensioning are discussed at the end of the paper.