Information Propagation Speed in Mobile and Delay Tolerant Networks

The goal of this paper is to increase our understanding of the fundamental performance limits of mobile and Delay Tolerant Networks (DTNs), where end-to-end multi-hop paths may not exist and communication routes may only be available through time and mobility. We use analytical tools to derive generic theoretical upper bounds for the information propagation speed in large scale mobile and intermittently connected networks. In other words, we upper-bound the optimal performance, in terms of delay, that can be achieved using any routing algorithm. We then show how our analysis can be applied to specific mobility and graph models to obtain specific analytical estimates. In particular, in two-dimensional networks, when nodes move at a maximum speed $v$ and their density $\nu$ is small (the network is sparse and surely disconnected), we prove that the information propagation speed is upper bounded by ($1+O(\nu^2))v$ in the random way-point model, while it is upper bounded by $O(\sqrt{\nu v} v)$ for other mobility models (random walk, Brownian motion). We also present simulations that confirm the validity of the bounds in these scenarios. Finally, we generalize our results to one-dimensional and three-dimensional networks.