Reliability evaluation of time evolving Delay Tolerant Networks based on Sum-of-Disjoint products

Network reliability evaluation of Delay Tolerant Networks (DTNs) is a challenging task due to their inherent features like node mobility, dynamically changing network topology and existence of highly disruptive environmental conditions etc. The research so far on such time-evolving dynamic networks mainly focusses on topology control, routing and information propagation with a little attention paid towards computing their overall network reliability. In this paper, we model DTNs by using Time Aggregated Graph and propose the notion of time-stamped-minimal path sets between a given source-destination pair of nodes, besides, providing a simple yet novel method to enumerate them. Further, by employing Multiple Variable Inversion-Sum of Disjoint Products algorithm, we obtain disjointed time-stamped-minimal path sets, which have a one-to-one mapping with the overall reliability expression of such time evolving networks. For obtaining instances of a DTN during an operational period, we resort to Monte Carlo Simulation to simulate the dynamically changing topology and other probabilistically varying network aspects. The simulation results demonstrate the efficacy of our proposal. At the end, we also present some initial investigation and insight on the time-stamped-minimal cut sets and problem in enumerating them, and infer that the usual notion of cut sets seems inapplicable for dynamic networks.