A Graph-Based Model for Disconnected Ad Hoc Networks

Abstract

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 Erdös-Renyi random graphs. Furthermore, we show that, under a uniformity assumption, the time taken for the connectivity graph to become connected scales as Θ( n log n λ ) with the number of nodes in the network. Hence we found that, using epidemic routing techniques, message delay is O( n log 2 n λ log log n ). The model is validated by numerical simulations and by a comparison with the connectivity patterns emerging from real experiments.

Broadcast delay of epidemic routing in intermittently connected networks

“…We now discuss our delay bounds, in comparison with the results of previous work, derived under the frequently used hypothesis of exponentially distributed and independent meeting times [2], [3], [10], [12]. Groenevelt et al [3] use a Markovian model based on the hypothesis that inter-meeting times for each pair of nodes are i.i.d.…”

“…The authors of [10] introduced an Erdös-Rényi graph model, justified by a similar hypothesis on exponentially distributed and independent intra-meeting times, in order to upper bound the delay of epidemic routing. In this case, the intra-meeting intensity (the rate at which any two of the network nodes meet) is assumed constant and independent of the number of nodes in the network, but a tentative generalization (by scaling the radio range or the node speeds) yields roughly the same scaling estimates for the delay as [3], [12].…”

“…In order to study the properties of intermittently connected networks, we are interested in sparse networks, as we will investigate the case where the normalized node density nR 2 n A is small (with R n the maximum radio range). Indeed, due to their potential applications, most of research on ICNs focuses on sparse mobile ad hoc networks (see [10]), a domain where intermittent connectivity is due to node mobility and to limited radio coverage.…”

“…The delivery delay of epidemic routing has been analyzed under various modeling assumptions [3], [7], [10], [12]. More recently, some papers have focused on information propagation in large disconnected mobile networks [4], [5], [8].…”

Eigenvector Centrality in Highly Partitioned Mobile Networks: Principles and Applications

“…On the other hand, such value determines the time horizon over which the system is able to deliver messages, placing therefore a constraint on the class of applications which can be supported by the system. Recent results by the first two authors [18] show that, given a system with n nodes and where meetings take place at intensity λ 5 , it can be shown under some independence assumptions that a phase transition takes place at T given by:…”