Arrival and departure processes of nodes in P2P systems

Since the departure of nodes has a large effect on the integrity of a P2P system, there is a strong need for methods that can mitigate the effects of node departure. In this paper we model the departure process of nodes in a P2P system with a renewal process to determine the node departure time for several node departure distributions, and we present connection conditions for active nodes that compensate for node departures. The fact that the departure interval of nodes in a P2P system can be expressed in terms of residual lifetimes is used to derive the expected values of node departure time for several lifetime distributions of nodes. It is also shown that the Laplace transform of the number of departure nodes can be expressed in terms of the node lifetime distribution function. Furthermore, we present several stochastic conditions for connecting active nodes in response to node departures.