Capturing the Evolving Properties of Disconnected Mobile P2P Networks

The design of message routing algorithms and its performance evaluation in disconnected mobile P2P networks are challenging issues due to its high dynamic evolving topology. To capture the evolution of the connectivity properties of such networks, a Time-Evolving Graph (TEG) model is proposed in this paper. Our intuitive observation is that the connectivity graph of a dynamic network can be obtained from the union of every snapshots observed over a sequential of past time steps. To avoid losing the network connectivity information in all past evolution, each possible edge is weighted by a set of the 2-tuples which consist of the start time and the duration of each contact. We then present the TEG model through using discrete time Markov process to deal with the time dependencies of consecutive time-step indexed network snapshots. As a further simplification, the dynamic of each possible edge is seen as an independent birth-death process. In addition, given the observed sequence of time-step indexed data, the birth and death probability of each possible edge are estimated using Laplace's rule of succession. We note that a TEG eventually converges to an un-uniform random graph in which the birth probability of all possible edge follows a unique power law distribution. The TEG model is validated through the computation of all possible time-evolved end-to-end fastest paths existing in real experimental datasets.