The Stability Region of the Delay in Pareto Opportunistic Networks

The intermeeting time, i.e., the time between two consecutive contacts between a pair of nodes, plays a fundamental role in the delay of messages in opportunistic networks. A desirable property of message delay is that its expectation is finite, so that the performance of the system can be predicted. Unfortunately, when intermeeting times feature a Pareto distribution, this property does not always hold. In this paper, assuming heterogeneous mobility and Pareto intermeeting times, we provide a detailed analysis of the conditions for the expectation of message delay to be finite (i.e., to converge) when social-oblivious or social-aware forwarding schemes are used. More specifically, we consider different classes of social-oblivious and social-aware schemes, based on the number of hops allowed and the number of copies generated. Our main finding is that, in terms of convergence, allowing more than two hops may provide advantages only in the social-aware case. At the same time, we show that using a multi-copy scheme can in general improve the convergence of the expected delay. We also compare social-oblivious and social-aware strategies from the convergence standpoint and we prove that, depending on the mobility scenario considered, social-aware schemes may achieve convergence while social-oblivious cannot, and vice versa. Finally, we apply the derived convergence conditions to three popular contact data sets available in the literature (Cambridge, Infocom, and RollerNet), assessing the convergence of each class of forwarding protocols in these three cases.