Modelling inter-contact times in human social pervasive networks

Thanks to the diffusion of mobile user devices (e.g. smart- phones) with rich computation and networking capabilities, we are witnessing an increasing integration between the cy- ber world of devices and the physical world of users. In this perspective, a possible evolution of pervasive networking (throughout referred to as social pervasive networks, SPNs) might consist in closely mapping human social structures in the network of the devices. Links between devices would cor- respond to social relationships between users, and communi- cation events between devices would correspond to commu- nications between users. It can be shown that fundamental convergence properties of PSN forwarding protocols are de- termined by the distributions of inter-contact times between the individual nodes (i.e. the time elapsed between two suc- cessive communication events between the nodes). Individ- ual pairs inter-contact times are hard to completely chara- terise, while the distribution of the aggregate inter-contact times is often a much more convenient figure. However, the aggregate distribution is not always representative of the individual pairs distributions, such that using it to charac- terise the properties of PSN forwarding protocols might not be correct. In this paper we provide an analytical model showing the exact dependence between the two in heteroge- neous SPNs. Moreover, we use the model to i) study cases in which studying the aggregate distribution is not enough, and ii) find sufficient conditions that guarantee that study- ing the aggregate distribution is enough to characterise the properties of PSN forwarding protocols.