Automating the Mean-Field Method for Large Dynamic Gossip Networks

We investigate an abstraction method, called mean-field method, for the performance evaluation of dynamic networks with pairwise communication between nodes. It allows us to evaluate systems with very large numbers of nodes, that is, systems of a size where traditional performance evaluation methods fall short. While the mean-field analysis is well-established in epidemics and for chemical reaction systems, it is rarely used for communication networks because a mean-field model tends to abstract away the underlying topology. To represent topological information, however, we extend the mean-field analysis with the concept of classes of states. At the abstraction level of classes we define the network topology by means of connectivity between nodes. This enables us to encode physical node positions and model dynamic networks by allowing nodes to change their class membership whenever they make a local state transition. Based on these extensions, we derive and implement algorithms for automating a mean-field based performance evaluation.