Sateeshkrishna Dhuli

Sateeshkrishna Dhuli, Chakravarthy Gopi, Yatindra Nath Singh

Studying network robustness for wireless sensor networks(WSNs) is an exciting topic of research as sensor nodes often fail due to hardware degradation, resource constraints, and environmental changes. The application of spectral graph theory to networked systems has generated several important results. However, previous research has often failed to consider the network parameters, which is crucial to study the real network applications. Network criticality is one of the effective metrics to quantify the network robustness against such failures and attacks. In this work, we derive the exact formulas of network criticality for WSNs using r-nearest neighbor networks and we show the effect of nearest neighbors and network dimension on robustness using analytical and numerical evaluations. Furthermore, we also show how symmetric and static approximations can wrongly designate the network robustness when implemented to WSNs.

Sateeshkrishna Dhuli, Y. N. Singh

Average consensus algorithms compute the global average of sensor data in a distributed fashion using local sensor nodes. Simple execution, decentralized philosophy make these algorithms suitable for WSN scenarios. Most of the researchers have studied the average consensus algorithms by modeling the network as an undirected graph. But, WSNs in practice consist of asymmetric links and the undirected graph cannot model the asymmetric links. Therefore, these studies fail to study the actual performance of consensus algorithms on WSNs. In this paper, we model the WSN as a directed graph and derive the explicit formulas of the ring, torus, $r$-nearest neighbor ring, and $m$-dimensional torus networks. Numerical results subsequently demonstrate the accuracy of directed graph modeling. Further, we study the effect of asymmetric links, the number of nodes, network dimension, and node overhead on the convergence rate of average consensus algorithms.

Sateeshkrishna Dhuli, Fouzul Atik

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.

Sateeshkrishna Dhuli, Kumar Gaurav, Y. N. Singh

Average consensus algorithms can be implemented over wireless sensor networks (WSN), where global statistics can be computed using communications among sensor nodes locally. Simple execution, robustness to global topology changes due to frequent node failures and underlying distributed philosophy has made consensus algorithms more suitable to WSNs. Since these algorithms are iterative in nature, their performance is characterized by convergence speed. We study the convergence of the average consensus algorithms for WSNs using regular graphs. We obtained the analytical expressions for optimal consensus and convergence parameters which decides the convergence time for r-nearest neighbor cycle and torus networks. We have also derived the generalized expression for optimal consensus and convergence parameters for m-dimensional r-nearest neighbor torus networks. The obtained analytical results agree with the simulation results and shown the effect of network dimension, number of nodes and transmission radius on convergence time. This work provides the basic analytical tools for managing and controlling the performance of average consensus algorithm in the finite sized practical networks.