Analysis of gossip performance with copulas

We propose a novel framework for analyzing the dynamic performance of a gossip protocol on a graph through the use of copulas. Copulas are a statistical technique that express the joint distribution of a set of random variables as a function of their marginal distributions. Using a version of gossip appropriate for wireless networks, we model the system dynamics through equations expressed in terms of q(i,t), the probability that node i has not received by time t, and r(i,t), the probability that node i does not transmit at time t. The solution of the system equations can be used to predict the fraction of nodes that have received the message by time t, which is an important measure of gossip protocol performance. The analysis is verified with simulation results on four different network topologies: a grid, a random geometric graph, an Erdos-Renyi graph, and a small-world graph. The model captures the system dynamics of the gossip protocol very well over a wide range of conditions.