Analytical modeling of robustness and stochastic resilience of temporal small-world complex networks

Abstract

This article explores the impact of online/offline node processes and Byzantine failures on the resilience of small-world network models, considering the lifetime of network nodes. We present novel analytical equations for estimating the expected communication time before user and network isolation, offering a unique perspective on network resilience through the lens of user behavior and involvement. Unlike most analyses focusing on stationary conditions, we employ network renewal processes to model these occurrences in temporal small-world networks where nodes can be online or offline. Our analytical equations, based on node lifetime distributions, shed light on the likelihood of network isolation under these conditions, offering valuable insights for optimizing network design and management. The validation of our analytical models through extensive simulations not only underscores their accuracy but also paves the way for a deeper understanding of temporal network behavior and resilience beyond the small-world paradigm.