Gnutella: Topology Dynamics On Phase Space

In this paper, the topology dynamic of Gnutella is studied through phase space. The dynamic changes in peer degree are studied as a time series in two dimensional phase space which is defined as the number of connected leaves and the number of connected ultras. The reported degrees are concentrated in three special Software related regions that we named as Ultra Stable Region, Leaf Stable Region and Transition Belt. A method is proposed to classify degree traces in phase space into different classes. Connection churn then is studied along with the churn in degree. It shows that the topological structure of Gnutella is rather stable in its connection degree but not the topology itself. The connection drop rate is estimated and the live time of connections is inferred afterwards. M/M/m/m loss queue system is introduced to model the degree keeping process in Gnutella. This model revealed that the degree stable is ensured by large new connection efforts. In other words the stable in topological structure of Gnutella is a results of essential unstable in its topology. That opens a challenge to the basic design philosophy of this network.