Analysis of Distributed Average Consensus Algorithms for Robust IoT networks

Internet of Things(IoT) is a heterogeneous network consists of various physical objects such as large number of sensors, actuators, RFID tags, smart devices, and servers connected to the internet. IoT networks have potential applications in healthcare, transportation, smart home, and automotive industries. To realize the IoT applications, all these devices need to be dynamically cooperated and utilize their resources effectively in a distributed fashion. Consensus algorithms have attracted much research attention in recent years due to their simple execution, robustness to topology changes, and distributed philosophy. These algorithms are extensively utilized for synchronization, resource allocation, and security in IoT networks. Performance of the distributed consensus algorithms can be effectively quantified by the Convergence Time, Network Coherence, Maximum Communication Time-Delay. In this work, we model the IoT network as a q-triangular r-regular ring network as q-triangular topologies exhibit both small-world and scale-free features. Scale-free and small-world topologies widely applied for modelling IoT as these topologies are effectively resilient to random attacks. In this paper, we derive explicit expressions for all eigenvalues of Laplacian matrix for q-triangular r-regular networks. We then apply the obtained eigenvalues to determine the convergence time, network coherence, and maximum communication timedelay. Our analytical results indicate that the effects of noise and communication delay on the consensus process are negligible for q-triangular r-regular networks. We argue that q-triangulation operation is responsible for the strong robustness with respect to noise and communication time-delay in the proposed network topologies.