Participation and Departure Processes of Nodes in Connection Graph

Since the departure of users has a large effect on the integrity of shared files in a P2P system, there is a strong need for methods that can mitigate the effects of user departure. In this paper, introducing a graph to represent the file-sharing in a P2P system, we model the participation and departure processes of users with a renewal process to determine the node departure time. The fact that the departure interval of nodes in the introduced connection graph 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.