Node connectivity analysis in cloud-assisted IoT environments

Internet of Things (IoT) have gained much attention recently. However, the transmission behavior of nodes in such a cloud-assisted IoT environment is not well studied. In this work, we mainly address the problem of node connectivity analysis based on percolation theory. First, we investigate when it is possible for two nodes to communicate with each other. Based on the results from bond percolation in a two-dimensional lattice, as long as the probability is close less than 0.5 and each sub-square contains at least four nodes, percolation occurs. Then, the conditions for full connectivity in a network graph are established. How two adjacent sub-squares are connected differentiates this work from others. The full connectivity occurs almost surely if each sub-square contains at least one node and the probability of having an open sub-edge is no less than 0.3822. The proposed conditions for percolation and full connectivity are validated by simulations.