Performance Analysis of Gossip Algorithms for Large Scale Wireless Sensor Networks

Gossip algorithms are often considered suitable for wireless sensor networks (WSNs) because of their simplicity, fault tolerance, and adaptability to network changes. They are based on the idea of distributed information dissemination, where each node in the network periodically sends its information to randomly selected neighbors, leading to a rapid spread of information throughout the network. This approach helps reduce the communication overhead and ensures robustness against node failures. They have been commonly employed in WSNs owing to their low communication overheads and scalability. The time required for every node in the network to converge to the average of its initial value is called the average time. The average time is defined in terms of the second-largest eigenvalue of a stochastic matrix. Thus, estimating and analyzing the average time required for large-scale WSNs is computationally complex. This study derives explicit expressions of average time for WSNs and studies the effect of various network parameters such as communication link failures, topology changes, long-range links, network dimension, node transmission range, and network size. Our theoretical expressions substantially reduced the computational complexity of computing the average time to
$O\left(n^{-3}\right)$
. Furthermore, numerical results reveal that the long-range links and node transmission range of WSNs can significantly reduce average time, energy consumption, and absolute error for gossip algorithms.