How Robust Is a D2D-Based Messaging Service?

Motivated by the massive and increasing number of online messaging service users, the idea of utilizing shortrange device-to-device (D2D) communication has been adapted to the access of instant messaging services on-the-go, introducing a D2D-based messaging service (D2D-Msg) paradigm that promises higher data rate and longer battery life. The quality of message dissemination in such a new paradigm, however, remains largely unknown due to the open nature of the D2D environment. To address this, we define a node survival probability that captures the impact of random and targeted node failures due to the open wireless environment. Further, we define a secondary infection rate R* that measures how fast message propagates initially, and leverage a framework based on probability generating function to analyze R* under random and targeted failures. Numerical results show that the D2D-Msg is more robust against random failure, the targeted node failure favors communication graph with narrow degree distribution, and R* is proportional to the ratio between the number of message-receiving users to all users, which is a good metric for quantifying the D2D-Msg's robustness.