Exact Performance Measures for Peer-to-Peer Epidemic Information Diffusion

We consider peer-to-peer anti-entropy paradigms for epidemic information diffusion, namely pull, push and hybrid cases, and provide exact performance measures for them. Major benefits of the proposed epidemic algorithms are that they are fully distributed, utilize local information only via pair-wise interactions, and provide eventual consistency, scalability and communication topology-independence. Our contribution is the derivation of exact expressions for infection probabilities through elaborated counting techniques on a digraph. Considering the first passage times of a Markov chain based on these probabilities, we find the expected message delay experienced by each peer and its overall mean as a function of initial number of infectious peers. In terms of these criteria, the hybrid approach outperforms pull and push paradigms, and push is better than the pull case. Such theoretical results would be beneficial when integrating the models in several peer-to-peer distributed application scenarios.