From Pareto inter-contact times to residuals

Interactions between mobile users are the building blocks of a variety of emerging communication paradigms, among which opportunistic networking is one of the most promising. In opportunistic networks, the information propagates through pair-wise contacts between users, and hence the intercontact time, i.e., the time between two consecutive interactions between a pair of users, plays a key role in the latency of information propagation. Given that new message availability and actual communication are typically asynchronous, analytical models often rely on the concept of residual inter-contact time, i.e, the time left before the next communication opportunity, starting from a random point in time. The statistical properties of the inter-contact times determine those of the associated residual inter-contact time. Of particular interest is the case of intercontact times featuring a Pareto distribution, due to the great attention this case has received in the literature. In this letter we discuss how to compute the residual inter-contact time when the inter-contact process between a pair of nodes features a Pareto distribution and we show that our exact solution can significantly improve the results commonly used in the literature.