On computing the reliability of opportunistic multihop networks with Mobile relays

Opportunistic multihop networks with mobile relays recently have drawn much attention from researchers across the globe due to their wide applications in various challenging environments. However, because of their peculiar intrinsic features like lack of continuous connectivity, network partitioning, highly dynamic behavior, and long delays, it is very arduous to model and effectively capture the temporal variations of such networks with the help of classical graph models. In this work, we utilize an evolving graph to model the dynamic network and propose a matrix-based algorithm to generate all minimal path sets between every node pair of such network. We show that these time-stamped-minimal-path sets (TS-MPS) between each given source-destination node pair can be used, by utilizing the well-known Sum-of-Disjoint Products technique, to generate various reliability metrics of dynamic networks, ie, two-terminal reliability of dynamic network and its related metrics, ie, two-terminal reliabilities of the foremost, shortest, and fastest TS-MPS, and Expected Hop Count. We also introduce and compute a new network performance metric-Expected Slot Count. We use two illustrative examples of dynamic networks, one of four nodes, and the other of five nodes, to show the salient features of our technique to generate TS-MPS and reliability metrics