Multicast Scaling of Capacity and Energy Efficiency in Heterogeneous Wireless Sensor Networks

Motivated by the requirement of heterogeneity in the Internet of Things, we initiate the joint study of capacity and energy efficiency scaling laws in heterogeneous wireless sensor networks, and so on. The whole network is composed of n nodes scattered in a square region with side length L = n(alpha), and there are m = n(nu) home points {cj}(j=1)(m), where a generic home point c(j) generates q(j) nodes independently according to a stationary and rotationally invariant kernel k(c(j), .). Among the n nodes, we schedule n(s) independent multicast sessions each consisting of k - 1 destination nodes and one source node. According to the heterogeneity of nodes' distribution, we classify the network into two regimes: a cluster-dense regime and a cluster-sparse regime. For the cluster-dense regime, we construct single layer highway system using percolation theory and then build the multicast spanning tree for each multicast session. This scheme yields the Omega(n(1/2+(alpha-1/2)gamma) / n(s) root k) per-session multicast capacity. For the cluster-sparse regime, we partition the whole network plane into several layers and construct nested highway systems. The similar multicast spanning tree yields the Omega(n(1/2-(1-nu)gamma/2) / n(s) root k) per-session multicast capacity, where gamma is the power attenuation factor. Interestingly, we find that the bottleneck of multicast capacity attributes to the network region with largest node density, which provides a guideline for the deployment of sensor nodes in large-scale sensor networks. We further analyze the upper bound of multicast capacity and the per-session multicast energy efficiency. Using both synthetic networks and real-world networks (i.e., Greenorbs), we evaluate the asymptotic capacity and energy efficiency and find that the theoretical scaling laws are gracefully supported by the simulation results. To our best knowledge, this is the first work verifying the scaling laws using real-world large-scale sensor network data.