Modelling Inter-contact Times in Social Pervasive Networks

Thanks to the diffusion of mobile user devices (e.g. smart-phones) with rich computing and networking capabilities, we are witnessing an increasing integration between the cyber world of devices and the physical world of users. In this perspective, a possible evolution of pervasive networking (hereafter referred to as social pervasive networks, SPNs) consists in closely mapping human social structures in the network of the devices. Links between devices would correspond to social relationships between users, and communication events between devices would correspond to communications between users. It can be shown that fundamental convergence properties of SPN forwarding protocols are determined by the distributions of inter-contact times between the individual nodes (i.e. the time elapsed between two successive communication events between the nodes). Individual pairs inter-contact times are hard to completely charaterise, 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. Therefore using it to characterise the properties of SPN forwarding protocols might not be correct. In this paper we provide an analytical model based on fundamental models of human social networks from the anthropology literature, which shows the exact dependence between the two in heterogeneous SPNs. Moreover, we use the model to i) study cases in which analysing the aggregate distribution is not enough, and ii) find sufficient conditions that guarantee that studying the aggregate distribution is enough to characterise the properties of SPN forwarding protocols.