Analysis of individual pair and aggregate inter-contact times in heterogeneous opportunistic networks

Foundational work in the area of opportunistic networks has shown that the distribution of inter-contact times between pairs of nodes has a key impact on the network properties, e.g. in terms of convergence of forwarding protocols. Specifically, forwarding protocols may yield infinite expected delay if the inter-contact time distributions present a particularly heavy tail. While these results hold for the distributions of inter-contact times between individual pairs, most of the literature uses the aggregate distribution, i.e. the distribution obtained by considering the samples from all pairs together, to characterise the properties of opportunistic networks. In this paper we analyse when this approach is correct and when it is not. We study, through an analytical model, the dependence between the individual pair and the aggregate distributions. We show that the aggregate distribution can be way different from the distributions of individual pair inter-contact times. Therefore, using the former to characterise properties that depend on the latter is not correct in general, although this is correct in some cases. We substantiate this finding by analysing the most representative distributions characterising real opportunistic networks that have been reported in the literature based on trace analysis. We study networks whose aggregate inter-contact time distribution presents a heavy tail with or without exponential cutoff. We show that a exponential cutoff in the aggregate appears when the average inter-contact times of individual pairs are finite. We also show that, when individual pairs follow Pareto distributions, the aggregate distribution consistently presents a heavy tail. However, heavy tail aggregate distributions can also emerge in networks where individual pair inter-contact times are not heavy tailed, e.g. exponential or Pareto with exponential cutoff distributions. This constitutes a reassuring result, as it means that forwarding protocols do not necessarily diverge in the quite common case of networks whose aggregate inter-contact time distribution is heavy tailed

A Framework for Characterizing the Wireless and Mobile Network Continuum ∗

The vast majority of research in wireless and mobile (WAM) networking falls in the MANET (Mobile Ad Hoc Network) category, where end-to-end paths are the norm. More recently, research has focused on a different Disruption Tolerant Network (DTN) paradigm, where end-to-end paths are the exception and intermediate nodes may store data while waiting for transfer opportunities towards the destination. Protocols developed for MANETs are generally not appropriate for DTNs and vice versa, since the connectivity assumptions are so different. We make the simple but powerful observation that MANETs and DTNs fit into a continuum that generalizes these two previously distinct categories. In this paper, building on this observation, we develop a WAM continuum framework that goes further to scope the entire space of Wireless and Mobile networks so that a network can be characterized by its position in this continuum. Certain network equivalence classes can be defined over subsets of this WAM continuum. We instantiate our framework that allows network connectivity classification and show how that classification relates to routing. We illustrate our approach by applying it to networks described by traces and by mobility models. We also outline how our framework can be used to guide network design and operation