Characterising aggregate inter-contact times in heterogeneous opportunistic networks

A pioneering body of work in the area of mobile opportunis- tic networks has shown that characterising inter-contact times between pairs of nodes is crucial. In particular, when inter-contact times follow a power-law distribution, the expected delay of a large family of for- warding protocols may be infinite. The most common approach adopted in the literature to study inter-contact times consists in looking at the distribution of the inter-contact times aggregated over all nodes pairs, assuming it correctly represents the distributions of individual pairs. In this paper we challenge this assumption. We present an analytical model that describes the dependence between the individual pairs and the ag- gregate distributions. By using the model we show that in heterogeneous networks - when not all pairs contact patterns are the same - most of the time the aggregate distribution is not representative of the individual pairs distributions, and that looking at the aggregate can lead to com- pletely wrong conclusions on the key properties of the network. For ex- ample, we show that aggregate power-law inter-contact times (suggesting infinite expected delays) can frequently emerge in networks where indi- vidual pairs inter-contact times are exponentially distributed (meaning that the expected delay is finite). From a complementary standpoint, our results show that heterogeneity of individual pairs contact patterns plays a crucial role in determining the aggregate inter-contact times statistics, and that focusing on the latter only can be misleading.