On the Expected Connection Lifetime and Stochastic Resilience of Wireless Multi-Hop Networks

To understand how node mobility and Byzantine node failures affect connectivity of wireless multi-hop networks, this paper investigates resilience of geometric random graphs to lifetime-based node failure and derives the expected connection time before an end-user is isolated from the graph. Different from previous analytical studies, which mainly focused on the so called critical transmission range, our study sheds light on the resilience analysis from the perspective of end-user´s connection experiences. In the paper, we first introduce a simple but general node behavior model by a semi-Markov process. Then we apply the theory of renewal process to the degree of a generic node and analyze the stochastic property of node connection time. At last, we provide the probability that the node isolation event occurs within any end-user´s lifetime and a close-form approximation of the network resilience. Our analysis and numeric simulation results indicate that networks with heavy-tailed lifetime (such as Weibull) distributions provides no improvement than those with light-tailed (e.g., Exponential) distributions in terms of longer expected connection lifetime for any end-user. Further, node mobility has more significant impact than lifetime does.