Modelling Capacity Scaling of Wireless Social Networks by A Population-Based Social Formation Model

In this paper, we investigate capacity scaling laws of wireless social networks under the social-based session formation. We model a wireless social network as a three-layered structure, consisting of the physical layer , social layer, and session layer ; we propose a cross-layer distance&densityawaremodel, called thepopulation-based formation model , under which: 1) for each node vk, the number of its friends, denoted byqk, follows a Zipf’s distribution with friendship degree clustering exponent γ; 2) qk anchor pointsare independently chosen according to a probability distribution w ith density function proportional toE−β k,X , whereEk,X is the expected number of nodes (population) within the distance |vk−X | to vk, andβ is the clustering exponent of friendship formation; 3) finally,qk nodes respectively nearest to those qk anchor points are selected as the friends of vk. We present the density function of general social friendship distribu t on as the basis for addressing general capacity of wireless social networks. In particular we derive the social-broadcast capacity for homogeneous physical layer under both generalized physicalandprotocol interference models, taking in account general clustering exponents of both friendship de gree and friendship formation in a 2-dimensional parameter space, i.e., (γ, β) ∈ [0,∞)2.