A graph-based model for disconnected ad hoc networks

Recently, research on disconnected networks has been fostered by several studies on delay-tolerant networks, which are designed in order to sustain disconnected operations. We focus on the emerging notion of connectivity which exists in such networks, where the message exchange between nodes is enforced by leveraging storage capabilities at intermediate relays, with the aim of achieving connectivity over time. The problem, under the constraint of intermittent connectivity, is hence to devise efficient mechanisms for message delivery, and evaluate the performance thereof. In this paper, we introduce a graph-based model able to capture the evolution of the connectivity properties of such systems over time. We show that, for most networks of interest, such connectivity graphs can be modeled as Erdos-Renyi random graphs. Furthermore, we show that, under a uniformity assumption, the time taken for the connectivity graph to become connected scales as Theta(n log n / lambda) with the number of nodes in the network. Hence we found that, using epidemic routing techniques, message delay is O(n log(2) n / lambda log log n). The model is validated by numerical simulations and by a comparison with the connectivity patterns emerging from real experiments. Index Terms-wireless networks, connectivity graph, delay-tolerant networking, Erdos-Renyi graphs, message latency.