Modeling Hierarchical Gossiping in Reliable Multicast Protocols

Although much work has been done on the design of gossip-based protocols, how to model and analyze the performance of such protocols is still a challenging task. The performance of a gossip-based protocol is significantly affected by its key parameters, e.g. the fanout of nodes. Determining the setting of such parameters through mathematical models is a key issue in gossip-based reliable multicast protocols. In this paper, we propose a generalized hierarchical gossiping algorithm and develop a mathematical model based on generalized random graphs to evaluate the reliability of hierarchical gossiping. Using our mathematical model, we investigate the impact of the parameters, namely the fanout distributions at the two levels of hierarchy on the reliability of hierarchical gossiping. We also give the critical condition for guaranteeing the gossiping messages to be propagated from local subgroups to the whole group. Simulations have been carried out and the results show that our analytical model is effective and accurate. The results obtained can be used to guide the design of hierarchical gossip-based protocols.