From Isolation Time to Node Resilience: Impact of Cascades in D2D-based Social Networks

The ever-increasing traffic demand from social networking service (SNS) users and recent progress in device-to-device (D2D) technology have empowered a new D2D-based SNS paradigm, which enables multimedia content exchange via short-range wireless networking. In this paradigm, a small node failure may trigger a collection of rapidly-spreading isolation events called cascade-of-failures. Unlike existing works that studied the outcome of cascading failures from the spatial and probabilistic perspectives, this paper sheds light on the temporal properties of the cascade-of-failures. To do this, we introduce a maximum isolation time that quantifies the steps needed until the last node is isolated by the cascades, and then show that it scales non-monotonically to the fraction of initial survivors (non-failure nodes) and increases logarithmically with the network size. Then, we use the result to further analyze a node resilience metric, which is the likelihood that a node does not become isolated before its social networking session is finished. These findings, which are validated using numerical simulations, provide a temporal perspective of network performance that is valuable in the design of D2D-based SNSs yet still missing in the literature.