Residual Inter-Contact Time for Opportunistic Networks with Pareto Inter-Contact Time: Two Nodes Case

Opportunistic networks (OppNets) are appealing for many applications, such as wild life monitoring, disaster relief and mobile data offloading. In such a network, a message arriving at a mobile node could be transmitted to another mobile node when they opportunistically move into each other’s transmission range (called in contact), and after multi-hop similar transmissions the message will finally reach its destination. Therefore, for one message the time interval from its arrival at a mobile node to the time the mobile node contacts another node constitutes an essential part of the message’s whole delay. Thus, studying stochastic properties of this time interval between two nodes lays a solid foundation for evaluating the whole message delay in OppNets. Note that this time interval is within the time interval between two consecutive node contacts (called intercontact time) and it is also referred to as residual intercontact time. In this paper, we derive the closed-form distribution for residual inter-contact time. First, we formulate the contact process of a pair of mobile nodes as a renewal process, where the inter-contact time features the popular Pareto distribution. Then, we derive, based on the renewal theory, closed-form results for the transient distribution of residual inter-contact time and also its limiting distribution. Our theoretical results on distribution of residual intercontact time are validated by simulations.