Refined Mean Field Analysis: The Gossip Shuffle Protocol Revisited

Abstract

Gossip protocols form the basis of many smart collective adaptive systems. They are a class of fully decentralised, simple but robust protocols for the distribution of information throughout large scale networks with hundreds or thousands of nodes. Mean field analysis methods have made it possible to approximate and analyse performance aspects of such large scale protocols in an efficient way that is independent of the number of nodes in the network. Taking the gossip shuffle protocol as a benchmark, we evaluate a recently developed refined mean field approach. We illustrate the gain in accuracy this can provide for the analysis of medium size models analysing two key performance measures: replication and coverage. We also show that refined mean field analysis requires special attention to correctly capture the coordination aspects of the gossip shuffle protocol. Keywords: Mean field • Collective adaptive systems • Discrete time Markov chains • Gossip protocols • Self-organisation This research has been partially supported by the Italian MIUR project PRIN 2017FTXR7S "IT-MaTTerS" (Methods and Tools for Trustworthy Smart Systems).